A demonstration method for eddy currents in magnets and conductor tubes with varying geometric parameters

Abstract

A method for demonstrating eddy currents using magnets and conductor tubes with varying geometric parameters, belonging to the field of physics experiments, comprises a through-hole spherical magnet a, a through-hole spherical non-magnetic magnet b, two identical permeable tubes, and a vertical support. Its key features are: the through-hole spherical magnet a is formed by sintering hard magnetic material with equally spaced through-holes passing through its center on the sphere's surface; a lead block is fixed within one of these holes, and magnetization is performed on a magnetizing device along the direction of the lead block passing through the center of the sphere; the permeable tubes are made of columnar transparent organic plastic, aluminum, copper, iron, or superconducting material, with equally spaced smooth through-holes punched in their sidewalls; the two identical permeable conductor tubes are vertically fixed on the vertical support; by combining the derived magnetic reluctance formula and using the controlled variable method to change the radius and thickness of the permeable conductor tubes and the radius of the through-hole spherical magnet a, different eddy current magnetic reluctance effects are obtained, providing a certain reference for teaching and scientific research.

Description

Technical Field

[0001] This patent relates to a demonstration experimental method for tubular eddy currents, enabling extended research on eddy current experiments using a through-hole type spherical magnet whose center of gravity does not coincide with its geometric center in a vertical conductor tube, and belongs to the field of physical experiments. Background Technology

[0002] In university physics teaching, the demonstration of eddy current phenomena often involves a vertical aluminum or copper tube with a ring magnet sliding down its outer casing (Tsinghua University demonstration experiment). This demonstration is convenient for observing the falling magnet, but it is prone to friction. Our university's demonstration hall uses one of the series of achievements from Jilin University (a recipient of the first prize of the National Teaching Achievement Award): an eddy current tube demonstration instrument. This instrument uses a square magnet (aluminum iron boron) and an aluminum block placed inside a square cylindrical tube to demonstrate eddy current phenomena. During use, the square magnet and aluminum block often get stuck in the middle of the square tube. In recent years, cylindrical magnets have been commonly used, with a cylindrical magnet (neodymium iron boron) and an aluminum cylinder placed inside a vertical copper tube. During the experiment (falling motion), tilting occurs, and the magnet easily collides with the side wall of the tube, causing significant friction. Sometimes, rotation also occurs. The phenomena such as rotation, collision, and friction cannot guarantee the initial direction of the magnetic poles, leading students to raise various questions and doubts, affecting their confidence in the experimental demonstration. These experimental phenomena are difficult for university students to study in greater depth using their existing theories. Besides these purely technical problems that need to be overcome, university physics urgently needs an exploratory experiment that aligns with students' theoretical foundations, combining theoretical research with experimental design and experimentation to avoid blind experimentation and to conduct some quantitative research. This patent aims to solve the problem of demonstrating credible and obvious eddy current phenomena while ensuring that the magnet falls without tilting or colliding (maintaining the magnetic pole direction) and without getting stuck in the tube, and also expanding into a more comprehensive exploratory demonstration of the relationship between magnetic resistance and the magnet and eddy current tube. This patent was completed with the support of the National Natural Science Foundation of China (Project Nos. 11805107, 11405092), the Basic Research Funds for Higher Education Institutions of Heilongjiang Province (Project No. 135209251), and the Heilongjiang Provincial Higher Education Teaching Reform and Application Project (Project No. SJGY20170385). Summary of the Invention

[0003] This patent mainly addresses a series of problems in demonstrating eddy currents in conductor tubes. It primarily uses a through-hole type spherical magnet and a through-hole type spherical non-magnetic body with numerous symmetrical vent holes and counterweights to lower the center of gravity, conductor tubes with numerous vent holes on the sidewalls or conductor tubes without sidewall holes, and changes in the thickness, inner radius, and magnetization intensity of the spherical magnet to solve this problem.

[0004] This patented technical solution: A method for demonstrating eddy currents using magnets and conductor tubes with varying geometric parameters, mainly composed of a through-hole type spherical magnet a, a through-hole type spherical non-magnetic magnet b, two identical transparent conductor tubes (complete cylindrical straight tubes with uniformly distributed holes on the sidewalls and made of non-ferromagnetic material, also known as transparent non-ferromagnetic material conductor tubes; all tubes mentioned in this patent refer to cylindrical straight tubes), a vertical support, a horizontal table, and horizontal and vertical reference plates. Its characteristic is that the through-hole type spherical magnet a is a sphere made of hard magnetic material (neodymium iron boron), and the sphere's surface is sintered with through-holes passing through its center, formed by equal spacing. Then, a lead block (dense...) is... A lead block (with a density greater than that of a hard magnetic material) is implanted and fixed in a hole, the size of which matches the size of the lead block. Magnetization (N pole, S pole) is performed on the lead block along the direction passing through the center of the sphere (the diameter direction of the sphere) using a magnetizing device. The through-hole type spherical non-magnetic body b is an alloy or aluminum sphere of the same size as the through-hole type spherical magnet a, with equally spaced through-holes (for ventilation) passing through the center of the sphere. The diameter, spacing, and number of these through-holes are the same as those of the through-hole type spherical magnet a. The horizontal and vertical reference plates are fixed to a vertical support by straight rods; the horizontal and vertical reference plates are thin metal plates. The through-hole type spherical magnet a... Five different colored rings are drawn on the opposite surface of the through-hole spherical non-magnetic object b using a marker. One colored ring is drawn on the edge of the through-hole with the same diameter as the lead block. The other four colored rings are evenly distributed on the same plane (the colored rings are drawn on the edge of the through-hole or on the spherical surface) and perpendicular to the diameter of the sphere passing through the lead block. (From the side, one complete ring and two half rings can be seen. The three points form a plane, which can be used as the orientation of the through-hole spherical magnet a and the through-hole spherical non-magnetic object b). The size of the colored rings should be clearly visible for vertical release and observation on the transparent conductor. The state of falling in the tube, such as tilting or rotating, is described. The transparent conductor tube is a transparent non-ferromagnetic material conductor tube. The transparent conductor tube (non-ferromagnetic material) is a columnar aluminum tube or a columnar copper tube with equally spaced smooth through holes punched in the side wall (indoor light can see the inside from the side exterior, which is convenient for recording video with a video recorder and extracting and analyzing data on a computer). The through-hole type spherical magnet a and through-hole type spherical non-magnetic body b have the same structure and size, and their diameter is smaller than the inner diameter of the transparent conductor tube (generally about 2 mm). The interior of the transparent conductor tube and the exterior of the through-hole type spherical magnet a and through-hole type spherical non-magnetic body b are all smooth.The two identical transparent conductor tubes are homogeneous cylindrical straight tubes, each with graduations (or a meter stick is fixed to the outer wall of the transparent conductor tube along the generatrix, with the graduated side facing the observation direction to facilitate recording the spatiotemporal state of the through-hole spherical magnet a and the through-hole spherical non-magnet b using a video recorder). The two identical transparent conductor tubes are vertically fixed to a vertical support, which is fixed to a horizontal tabletop. The distance from the bottom (below) of the two identical transparent conductor tubes to the horizontal tabletop is greater than the diameters of the through-hole spherical magnet a and the through-hole spherical non-magnet b. There is a concave surface on the horizontal tabletop at the bottom of the two identical transparent conductor tubes. A pit is used to collect the through-hole spherical magnet a and the through-hole spherical non-magnetic object b when they fall onto the table. The inner surface of the pit is lined with sponge. A video recorder is fixed at a certain distance (determined based on device size and video resolution) directly opposite two vertical tubes, with the two tubes clearly visible in the video recorder's field of view. The video recorder is also fixed approximately 20cm directly above the two tubes, with its lens facing the central axis of the through-hole conductor tube. At the start of the experiment, the position, time, and state of the through-hole spherical magnet a and the through-hole spherical non-magnetic object b as they fall are recorded (all subsequent experimental recordings follow this pattern). Experimental demonstration:

[0005] Experiment 1) Hold a through-hole spherical magnet a and a through-hole spherical non-magnetic body b with both hands respectively, with the lead block facing down and at the same height, and release them from two identical transparent conductor tubes respectively. At the moment of release, the vertical axis of the center of the through-hole spherical magnet a and the through-hole spherical non-magnetic body b coincides with the central axis of the transparent conductor tube. Observe the phenomenon.

[0006] Experiment 2) Then, the through-hole type spherical magnet a and the through-hole type spherical non-magnetic body b demonstrated in Experiment 1) are interchanged and released simultaneously in two identical transparent conductor tubes. The direction with lead block 2 is facing downwards. At the moment of release, the vertical axis of the center of the through-hole type spherical magnet a and the through-hole type spherical non-magnetic body b coincides with the central axis of the transparent conductor tube. Observe the phenomenon. The experimental results show that the through-hole type spherical magnet a descends more slowly than the through-hole type spherical non-magnetic body b (it takes longer to pass through the tube).

[0007] Experiment 3) As shown in Figure 1(c), cut off 1 / 4 of the lower 1 / 3 of the transparent conductor copper tube from the side in the observation direction and observe the effect of the through-hole spherical magnet a falling in the vertically processed transparent conductor tube (it is seen that the speed of the through-hole spherical magnet a in the cut section is faster than that in the uncut section, that is, there is also eddy current in the cut section of the transparent conductor tube, but it is smaller than that in the uncut section).

[0008] Experiment 4) Replace the through-hole spherical magnet a and the through-hole spherical non-magnetic magnet b with solid homogeneous spherical magnet a and solid homogeneous spherical non-magnetic magnet b of the same size (the magnetization direction of the solid homogeneous spherical magnet a is also uniformly magnetized along the diameter direction through the center of the sphere). Replace the transparent conductor tube with a non-ferromagnetic material conductor tube with no holes in the sidewalls. Cut off 1 / 4 of the sidewall from the lower 1 / 3 of the tube in the observation direction. Repeat the operation process of Experiment 1) and Experiment 2). The main observation is to observe the motion state (trajectory, posture) of the solid homogeneous spherical magnet a and the solid homogeneous spherical non-magnetic magnet b falling in the vertical non-ferromagnetic material conductor tube with no holes in the sidewalls.

[0009] Note: In this patent specification, changes in physical parameters refer to experimental studies (controlled variable method) under the condition that other parameters remain unchanged. Release in the experiment refers to the release after the central vertical axis of the through-hole spherical non-magnetic body and the through-hole spherical magnet (or the solid spherical magnet and the solid spherical non-magnetic body) coincides with the central axis of the permeable tube (or the conductor tube with no sidewall holes). The "permeable tube" in this specification includes: permeable non-ferromagnetic material conductor tubes (e.g., copper tubes, aluminum tubes), permeable non-conductor tubes (e.g., transparent plastic tubes), permeable ferromagnetic material conductor tubes (e.g., iron material tubes), and permeable superconducting material tubes. Unless otherwise specified, the permeable conductor tube or conductor tube in this patent specification refers to a conductor tube made of non-ferromagnetic material.

[0010] Experiment 5) To conduct further research, the materials of the two identical transparent conductor tubes were replaced with (collectively referred to as: transparent tubes): transparent organic plastic material, aluminum material, copper material, iron material, and superconducting material. That is, the transparent tubes are homogeneous cylindrical straight tubes made of transparent organic plastic material, aluminum material, copper material, iron material, and superconducting material, respectively. The transparent tubes are of the same size, wall thickness, and structure. Smooth through-holes of the same size and evenly spaced are drilled into the sidewalls of the tubes. In other words, the transparent tubes include: transparent non-ferromagnetic material conductor tubes, transparent non-conductor tubes, transparent ferromagnetic material conductor tubes, and transparent superconducting material tubes. Experiments 1) and 2) were repeated, and the eddy current effects of different material transparent tubes were compared. Holding a through-hole spherical magnet a and a through-hole spherical non-magnetic magnet b in each hand, and releasing them simultaneously from the same height with the lead block facing downwards, the following observations were made:

[0011] (1) In the case of a transparent organic plastic tube, the falling speed of the through-hole spherical magnet a and the through-hole spherical non-magnetic body b tends to be the same; (2) In the case of aluminum, the through-hole spherical magnet a falls slower than the through-hole spherical non-magnetic body b; (3) In the case of copper, the through-hole spherical magnet a falls slower than the through-hole spherical non-magnetic body b (and slower than in the case of aluminum tube); (4) In the case of iron tube, the through-hole spherical magnet a falls slower than the through-hole spherical non-magnetic body b, and may even be attracted to the tube wall and remain stationary; (5) In the case of superconducting materials, if they are placed in a superconducting state, a through-hole spherical magnet a will be suspended at the tube port (the superconducting tube has perfect diamagnetism, and its descent speed tends to zero). Alternatively, if the through-hole spherical magnet a is replaced with a through-hole spherical superconducting sphere of the same size and placed in a superconducting state, and the transparent superconducting material tube is replaced with a strong magnet tube (the magnetic poles of the strong magnet tube are parallel to the central axis of the tube, and the through-hole spherical superconducting sphere has perfect diamagnetism, and its descent speed tends to zero), the through-hole spherical superconducting sphere will be suspended at the tube port.

[0012] Experiment 6) A through-hole spherical non-magnetic body b (or a solid non-magnetic body b whose center of mass coincides with the center of the sphere), a through-hole spherical magnet a (or a solid magnet a uniformly magnetized body whose center of mass coincides with the center of the sphere), the magnetization intensity vector of the magnet is M0 (or the magnet surface B in the magnetization direction is constant, such as B = 0.1 Tesla, 0.5 Tesla), the magnet radius is R0 (such as 20 mm), the wall thickness of the through-hole conductor tube 1 (or conductor tube 1) is b (2 mm), and the resistivity of the conductor tube (non-ferromagnetic material) is constant (such as commonly used aluminum, copper materials), the length of the through-hole conductor tube (or conductor tube without side walls) is constant (such as 1 meter high) [or as shown in Figure 1(c) and Figure 1(c)]. d) The length of the transparent conductor tube (or the conductor tube without side holes) is fixed (e.g., 1 meter high). The lower 1 / 3 of the transparent conductor tube (or conductor tube) is cut off from the side in the observation direction by 1 / 4 of the side. Ten sizes of transparent conductor tubes (or conductor tubes without side holes) of the same material are made (20 in total, 2 of the same size). The inner radii r are R0(1+0.1), R0(1+0.2), R0(1+0.3), R0(1+0.4), R0(1+0.5), R0(1+0.6), R0(1+0.7), R0(1+0.8), R0(1+0.9), and R0(1+1); where R0 is the radius of the magnet.

[0013] Repeat the operation procedures of Experiment 1) and Experiment 2). Hold a through-hole spherical magnet a and a through-hole spherical non-magnetic magnet b, or two solid spherical magnets and a solid spherical non-magnetic magnet of the same size, in each hand. Release the through-hole spherical magnet a with the magnetization direction facing downwards at the same height. That is, release the through-hole spherical non-magnetic magnet and the through-hole spherical magnet or the solid spherical magnet and the solid spherical non-magnetic magnet after their central vertical axes coincide with the central axis of the through-hole conductor tube or the conductor tube with no holes in the sidewalls. Record the position, time and state of the through-hole spherical magnet a and the through-hole spherical non-magnetic magnet b with a fixed video recorder.

[0014] Experiment 7) A through-hole spherical non-magnetic body b (or a solid non-magnetic body b whose center of mass coincides with the center of the sphere), a through-hole spherical magnet a (or a solid magnet a uniformly magnetized body whose center of mass coincides with the center of the sphere), the magnetization vector of the magnet is M0 (or the magnet surface B in the magnetization direction is constant, such as B = 0.1 Tesla, 0.5 Tesla), the magnet radius is R0 (such as 20 mm), the wall thickness of the through-hole conductor tube (or the conductor tube without side holes) is b, and the resistivity of the conductor tube (non-ferromagnetic material) is ρ (such as commonly used aluminum or copper materials) remains constant. The length of the tube is fixed (e.g., 1 meter high) [or as shown in Figures 1(c) and 1(d), the length of the through conductor tube (or the conductor tube without side walls) is fixed (e.g., 1 meter high), and the lower 1 / 3 of the through conductor tube (or the conductor tube) is cut off from the side in the observation direction by 1 / 4 of the side]. Ten sizes (20 in total, 2 of the same size) of the through conductor tube (or the conductor tube without side walls) of the same material are made, with tube wall thickness b of 1mm, 1.5mm, 2mm, 2.5mm, 3mm, 3.5mm, 4mm, 4.5mm, 5mm, and 5.5mm respectively.

[0015] Repeat the procedures of Experiments 1) and 2). Hold a through-hole spherical magnet a and a through-hole spherical non-magnetic magnet b, or two solid spherical magnets and a solid spherical non-magnetic magnet of the same size, in each hand. Release the through-hole spherical magnet a with the magnetized direction facing downwards at the same height. That is, release the through-hole spherical non-magnetic magnet and the through-hole spherical magnet or the solid spherical magnet and the solid spherical non-magnetic magnet after their central vertical axes coincide with the central axis of the through-conductor tube or the conductor tube without side holes. Record the position, time, and state of the through-hole spherical magnet a and the through-hole spherical non-magnetic magnet b with a fixed video recorder.

[0016] Regarding the analysis of tilting (flipping effect) rotation, eddy currents are generated in the conductor during the magnet's motion relative to the conductor. Thus, regardless of whether the magnet is square or cylindrical, it experiences magnetic resistance from the eddy currents induced in the conductor tube near its upper and lower ends. Besides the eddy current resistance and the magnet's weight, there is also air resistance during the fall (due to the asymmetry of the gap between the magnet and the tube). This magnetic resistance causes a flipping torque (torque M = P) on the magnet's center of mass. m ×B, P m It is the magnetic moment, that is, P mA magnetic torque occurs when the magnetic field is not parallel to the magnetic induction intensity B or when the magnetic field in the tube is not uniform, causing the magnet's axis to not coincide with the tube's central axis. In addition, the Earth's magnetic field also exerts a magnetic torque on the magnet; the greater the height of a square or cylindrical magnet, the greater the magnetic torque, exhibiting a reversal effect that parallels the magnet to the Earth's magnetic field. Air resistance is also a factor contributing to this reversal torque effect. This causes the magnet to tilt during its descent, leading to significant friction against the side walls. Once tilted, it may rub against the side walls or even become stuck in the tube, affecting the experimental results (although the height of a cylindrical magnet is usually greater than its diameter). Similarly, for non-magnetic objects, in addition to gravity, there is air resistance during descent (due to the asymmetry of the gap between the non-magnetic object and the tube). This air resistance causes a reversal torque on the center of mass of the non-magnetic object. (Meanwhile, for non-magnetic objects made of conductive materials, they are also affected by the Earth's magnetic field and the surrounding electromagnetic environment.) The magnetic drag effect of the generated eddy currents, as well as the Coriolis force generated by the falling object itself and the airflow in the tube due to the Earth's rotation, are factors that have been previously overlooked. Although relatively weak, their cumulative effect is still significant. These factors can all cause deviations, deflections, or rotations in the object's trajectory. Non-magnetic objects may also tilt during the fall, leading to greater friction against the side walls and even getting stuck in the tube, affecting the experimental results. In the design, it is desirable for the eddy currents to be more pronounced, thus reducing the gap between the magnet and the tube. However, friction issues can easily cause many questions for students. If the gap is increased, problems such as magnets or non-magnetic objects tilting and getting stuck in the tube may occur (if the gap is too large, the magnetic field resistance of the magnet in the eddy current tube decreases, and the path deviates from the vertical, causing it to collide with the vertical tube side walls). The above analysis addresses the problems that occurred when the geometric center and the center of gravity coincided in previous literature. The magnet in this patent is a spherical magnet with spherical symmetry and a through-hole design (or a non-magnetic spherical magnet with a through-hole design). During its fall, there is a gap between the magnet and the conductor tube (with holes in the sidewalls), and the magnet or non-magnetic magnet has uniform through-holes, which reduces air resistance and the influence of the Coriolis force (the deviation of the Coriolis force from the object itself is almost negligible due to the short fall distance). This reduces the overturning torque of the air on the geometric center (the center of gravity in a homogeneous case). Furthermore, the current induced in the eddy current tube (conductor tube) and the geomagnetic field generate a magnetic torque on the through-hole spherical magnet, so even if there is a tendency to overturn (tilt), because... The center of gravity of the through-hole spherical magnet generates a gravitational torque below its geometric center, which counteracts the tilting effect (counteracting the overturning torque generated by air resistance and magnetic resistance) and maintains it in its initial state (the initial downward-facing release state of the through-hole spherical magnet and the through-hole spherical non-magnetic body). Since the falling body is spherical, there will be no impact on the experimental results due to overturning (tilting) and getting stuck in the conductor tube (or colliding and rubbing against the side wall). At the same time, the downward shift of the center of gravity of the through-hole spherical magnet also prevents the air inside the tube from passing through the sphere due to overturning (tilting) (achieving the sphere to maintain its initial orientation as much as possible).

[0017] Without altering the original square or cylindrical shape of the experimental magnet (or non-magnetic object) (currently homogeneous, square, or cylindrical), adding a counterweight to the bottom of the magnet (or non-magnetic object) to make its center of gravity much lower than its geometric center is necessary to avoid the problem of it getting stuck in the tube; alternatively, the dimensions of the experimental magnet (or non-magnetic object) could be much smaller than the inner diameter of the tube, but in this case, the eddy currents are weak, making it difficult to observe the phenomenon; or the cylinder could be made so that its height is much smaller than its diameter, like a one-yuan coin (although it wouldn't get stuck, multiple factors would interfere, making it difficult for students to understand, and the asymmetrical airflow due to air resistance would also have an impact, while we want to demonstrate the phenomenon generated by eddy currents); see attached. Figure 2 The experiment involves placing a square or cylindrical magnet (or non-magnetic object) into a transparent conducting tube, and then placing the cylindrical object into a thin, coin-like disc with a height (thickness) much smaller than its diameter. Due to the asymmetry of the gap between the tube wall and the thin cylindrical disc, the thin cylindrical disc initially deflects due to air resistance during its fall. The non-magnetic thin cylindrical disc then stabilizes from a horizontal to a vertical position during its fall (while the magnetic thin cylindrical disc is also subject to the resistance of the eddy current magnetic field in the conducting tube, resulting in a different fall). The deflection angles of the magnetic and non-magnetic thin cylindrical discs during their fall are different, and they experience different air resistance. Therefore, it is not easy to use a thin cylindrical magnet to demonstrate a comparative eddy current phenomenon.

[0018] Regarding the analysis of magnetic reluctance, in the case of a spherical magnet (the through-hole spherical magnet has symmetrically and uniformly distributed through-holes, which can be approximated as a solid homogeneous spherical magnet to handle the magnetic field), the analysis of the factors affecting the magnetic reluctance generated by the eddy currents in the conductor tube is as follows: Figure 4 In the case of axisymmetric coordinates, spherical coordinates are used Indicates that the operator Where e R e θ , Radial R, polar angle θ, and azimuth angle, respectively. The unit vector. Let a spherical ferromagnetic material (e.g., neodymium iron boron) be uniformly magnetized, with magnetization vector M0, radius R0, and external magnetomotive force... and the magnetic potential inside the sphere They all satisfy the Laplace equation.

[0019]

[0020] The corresponding magnetic potential outside the sphere must decrease as the distance increases, therefore its expansion contains only negative R terms.

[0021]

[0022] The magnetic potential inside the sphere is finite when R = 0, therefore it contains only terms that are positive powers of R.

[0023]

[0024] in a n and b n For P n (cosθ) coefficient

[0025] From the boundary conditions when R = R0

[0026] Magnetic induction intensity B 1R =B 2R (B 1R B 2R (respectively, outside and inside the sphere)

[0027] Magnetic field strength H 1θ =H 2θ ((H 1θ H 2θ or (respectively, outside and inside the sphere)

[0028] Assuming the area outside the sphere is a vacuum, we have

[0029] Substituting the boundary conditions and expanding, the comparison (omitted) P n The coefficient of (cosθ) is obtained

[0030] a n =b n =0 (n≠1)

[0031] Calculate the external magnetic potential of the sphere

[0032] Will Substitution

[0033]

[0034]

[0035]

[0036] The magnetic flux density component at a distance R from the center of the sphere is obtained.

[0037]

[0038]

[0039]

[0040] The magnitude of the projection onto the magnet's axis of symmetry and perpendicular to that axis (that is, the projection along the normal to the sidewall of the conductor tube, which is also the magnetic flux density component affecting the electromotive force and magnetic reluctance)

[0041] (Near the surface of the sphere R = R0, the maximum magnetic flux density is in the direction of θ = 0, and the minimum magnetic flux density is in the direction of θ = 90 degrees.)

[0042] That is, the magnitude of the magnetic induction intensity at point p, a distance R from the center of the spherical magnet in a conducting tube (or other non-conducting tube), perpendicular to the side wall of the conducting tube, is: (Generates an effective magnetic field with magnetic resistance along the axis of the conductor tube)

[0043]

[0044] For ease of research, see attached Figure 5 A conductor tube is placed vertically for a sufficient length, with the center of a spherical magnet coinciding with the central axis of the tube. The magnet descends at a velocity v parallel to the central axis of the tube. Let the magnitude of the magnetic field strength through the tube be B, the tube's infinitesimal height be dh, the magnet's descent velocity be v, and the angle between the magnetic field strength B and the tube's infinitesimal height dh (or the angle between the magnet's descent velocity v and the magnetic field strength B) be β. The resistivity of the tube is ρ, the thickness is b, and the inner radius is r (considering that the thickness b << r, we take that the magnitude of the magnetic field strength B is equal within the infinitesimal height dh and the ring of thickness b). Then, the magnitude of the electromotive force generated on the conducting ring of radius r and infinitesimal height dh is...

[0045]

[0046] The resistance of the conductor ring at a height of infinitesimal element dh on the conductor tube (for ease of integration, the inverse of the resistance is taken as the integral). Consider b << r, expand

[0047] (For the resistance of a transparent conductor tube and a conductor tube without sidewalls) The only difference is a coefficient related to the distribution density and aperture size of the holes. If the number of holes in the transparent conductor tube is relatively small, it can be approximated by a resistor. The problem being studied remains unaffected; of course, the resistance of a transparent conductor tube can also be experimentally measured by cutting the same transparent conductor tube along its generatrix.

[0048] Current intensity on a conductor ring of infinitesimal height dh in a conductor tube

[0049]

[0050] The current induced in the conductor tube generates a magnetic force (Ampere force, magnetic reluctance). This force is symmetrical about the central axis of the conductor tube (B is perpendicular to the conductor ring, and the Ampere force is perpendicular to B and the flow direction dI). The forces perpendicular to the central axis of the conductor tube cancel each other out, leaving only the Ampere force parallel to the central axis of the conductor tube.

[0051]

[0052]

[0053] The volume of the conductor ring with a height of infinitesimal element dh on the conductor tube is dV = bdh / 2πr.

[0054] It can be seen that, for the magnetic induction intensity of a spherical magnet acting on a conducting tube (which is also the magnitude of the interaction force exerted on the magnet by the magnetic field of the current excited in the conducting tube), given the basic parameters of the spherical magnet (magnetization vector M0, radius R0), the magnitude of the magnetic induction intensity perpendicular to the sidewall of the conducting tube at a radius r (inner diameter) p (distance R from the center of the spherical magnet) is:

[0055]

[0056] Wherein, the geometric relations are R = r / sinθ and h = r / tanθ.

[0057] Substitution The conclusion is

[0058]

[0059] The magnetic reluctance F generated by the current induced in the conducting tube is the magnitude of the magnetic reluctance generated by the current induced in the conducting tube, which is the boundary between the upper and lower parts of the spherical magnet (the horizontal plane passing through the center of the spherical magnet).

[0060]

[0061] in

[0062]

[0063] Based on the above analysis, during the magnet's descent (assuming the conductor tube is sufficiently long, for a finite conductor tube...), it is only... (The upper and lower limits of integration change) The spatial scale range of the conductor tube pierced by the magnetic field below the horizontal plane passing through the center of the magnet (through-hole spherical magnet) (and the magnetic field above the horizontal plane passing through the center of the magnet) remains unchanged (although the relative positions change, the spatial scale range of the conductor tube pierced by the magnetic field of the magnet (through-hole spherical magnet) remains unchanged, therefore, what affects the magnetic reluctance is: the magnetization vector M0 of the magnet (through-hole spherical magnet a), the radius R0 of the magnet (spherical magnet a), the falling velocity v of the magnet (through-hole spherical magnet), the thickness b of the conductor tube, the inner radius r of the conductor tube, the resistivity ρ of the conductor tube (material property of the conductor, such as aluminum, copper, superconducting state), and μ0 is the permeability of vacuum. It can be seen that, on a structural scale, the changes in the inner radius r of the conductor tube and the radius R0 of the magnet have a significant impact on the magnetic reluctance (1 / r 4 , As r→R0,

[0064] Regarding the spatiotemporal analysis of the fall, the laws governing the fall of a through-hole spherical non-magnetic body (mass m1) are established, with downward as the positive direction of the position coordinate h, air resistance -k1v1, air resistance coefficient k1, and the falling velocity v1 of the through-hole spherical non-magnetic body.

[0065]

[0066] When t = 0, v1 = 0, h(non-magnetic body) = 0, (the position coordinates of the non-magnetic body are denoted as h1 = h(non-magnetic body)).

[0067]

[0068] Position-time equation of non-magnetic body

[0069] The falling process of a through-hole spherical magnet is analyzed, with downward as the positive direction of position coordinate h, air resistance -k1v, eddy current resistance F = kv, and the falling velocity v of the through-hole spherical magnet (mass m).

[0070]

[0071] Taking t=0, v=0, h(magnet)=0, we get

[0072]

[0073] Position-time equation of a magnet

[0074] It can be seen that the magnet's closing velocity Less than the tail velocity of a non-magnetic body In the experiment, the air drag coefficient k1 was relatively small, and the tail velocity of the magnet was affected by the magnetic drag coefficient. The impact is significant. In actual experiments, the expression can be derived based on this patent. or By designing and verifying experiments with the corresponding physical parameters, we can fundamentally resolve some long-standing confusion among our colleagues regarding the relationship between magnetic resistance and the magnet and the conductor tube in demonstration experiments. Furthermore, by applying the conclusions drawn from this patented spherical magnet to comparative studies in teaching, combining them with the phenomena and data observed during the fall of spherical magnets, and conducting cyclical research from theory to practice and back again, we can achieve a highly meaningful outcome.

[0075] The beneficial effects of this patent are: (1) Due to the external design of the spherical body (through-hole type spherical magnet) and the many symmetrical ventilation holes in the sphere, plus the sidewall of the conductor tube which is also a lot of ventilation holes (and observation holes), the falling process of the magnet or non-magnetic body can reduce the influence of air resistance; it also eliminates the vortex (Coriolis force) generated by the rising airflow around the through-hole type spherical magnet (or non-magnetic body) and causes it to rotate; (2) At the same time, due to the downward shift of the center of mass (the center of mass of the lead block is below the geometric center), the gravitational torque (the gravitational torque about the geometric center of the sphere when deflecting) weakens the flipping torque (flipping effect) of air and magnetic resistance on the geometric center of the sphere. Even if there is a flipping (tilting) effect, because it is a sphere Therefore, there will be no situation where the ball gets stuck in the conductor tube due to tilting and flipping (or collision with the side wall friction), affecting the experimental results; (3) It ensures that the magnetic pole direction remains unchanged during the falling process of the magnet, which simplifies the analysis of theoretical problems (without problems such as the rotating magnetic field when the magnet falls), and is more suitable for the innovative research of college students; (4) Sponge is pasted on the inner surface of the pit to prevent the ball from falling onto the horizontal table and rolling off the table; (5) The materials of the two identical transparent tubes are: transparent organic plastic material, aluminum material, copper material, iron material, and superconducting material, respectively. The magnetic resistance phenomenon of different types of materials such as aluminum material, copper material, iron material, and superconducting material can be seen, as well as the perfect diamagnetism of superconductors; (6) By It is clearly understood that the magnetic reluctance generated by the eddy currents in the eddy current tube (conductor tube) is determined by the magnetization vector M0 of the (through-hole spherical magnet or solid spherical magnet), the magnet radius R0, the magnet's falling velocity v, the conductor tube's thickness b, the conductor tube's inner radius r, and the conductor tube's resistivity ρ (the conductor's material properties, such as aluminum, copper, or superconductivity). This leads to a design scheme that addresses the influence of magnetic reluctance. This patent exhibits significant features and substantial advancements compared to existing technologies. It is ingeniously conceived, low-cost, and easy to implement. In teaching, it expands students' thinking, cultivates their innovative awareness and practical spirit, and its widespread application in education will enhance its educational value. Attached Figure Description

[0076] Figure 1(c) shows a schematic diagram of the structure of the through conductor tube (through tube) after processing;

[0077] Figure 1(d) shows a schematic diagram of the structure of the conductor tube (a non-permeable tube with no holes in the sidewalls) after processing;

[0078] Appendix Figure 2 A schematic diagram of the falling process of a square or cylindrical (thin cylindrical) sheet;

[0079] Appendix Figure 3 The following is a schematic diagram of the structure of this patent. The reference numerals are as follows: 1. Transparent conductor tube (transparent non-ferromagnetic material conductor tube), transparent tube [including: transparent non-ferromagnetic material conductor tube (e.g., copper tube, aluminum tube), transparent non-conductor tube (e.g., transparent plastic tube), transparent ferromagnetic material conductor tube (e.g., iron material tube), transparent superconducting material tube)], non-ferromagnetic material conductor tube with no sidewall pores, non-conductor tube with no sidewall pores (e.g., transparent plastic tube), ferromagnetic material conductor tube with no sidewall pores (e.g., iron material tube), superconducting material tube], 2. Lead block, 3. Vertical support, 4. Horizontal tabletop, 5. Recess, 6. Horizontal and vertical reference plates, 7. Dyed ring (top ring), 7-1. Dyed ring (side ring);

[0080] Appendix Figure 4 Magnetic induction intensity pattern analysis diagram;

[0081] Appendix Figure 5 Magnetic resistance calculation and analysis diagram;

[0082] Appendix Figure 6 Schematic diagram of a small magnetic ring magnet position recording device. Reference numerals: 8. Small magnetic ring; 9. A straight rod made of smooth, non-ferromagnetic material with graduations. Detailed Implementation

[0083] As attached Figure 3A method for demonstrating eddy currents in a magnet and conductor tube with variable geometric parameters is mainly composed of a through-hole spherical magnet a, a through-hole spherical non-magnetic magnet b, two identical transparent conductor tubes 1 (non-ferromagnetic material, also known as: transparent non-ferromagnetic material conductor tube 1), a vertical support 3, a horizontal tabletop 4, and horizontal and vertical reference plates 6. Its characteristic is that the through-hole spherical magnet a is a sphere made of hard magnetic material (neodymium iron boron), and through-holes passing through the center of the sphere are punched at equal intervals on the surface of the sphere and sintered. A lead block 2 (with a density greater than that of the hard magnetic material) is then inserted and fixed into one of the holes. The size of the hole... The lead block 2 is matched in size and is magnetized (N pole, S pole) along the direction through the center of the sphere (the diameter direction of the sphere) on the magnetizing device; the through-hole type spherical non-magnetic body b is an alloy or aluminum sphere of the same size as the through-hole type spherical magnet a, with through holes (for ventilation) equally spaced through the center of the sphere on its surface, the diameter, spacing and number of the through holes being the same as those of the through-hole type spherical magnet a; the horizontal and vertical reference plates 6 are fixed to the vertical support 3 by straight rods, and the horizontal and vertical reference plates 6 are thin metal plates; the through-hole type spherical magnet a and the through-hole type spherical non-magnetic body b On the surface opposite lead block 2, use a marker to paint 5 different colored rings (different colors to distinguish different rings). One colored ring 7 (top ring) is painted on the edge of the through hole with the same diameter as lead block 2. The other 4 colored rings 7-1 (side rings) are evenly distributed in the same plane (the colored rings are painted on the edge of the through hole or on the spherical surface) and perpendicular to the spherical surface passing through the diameter of lead block 2 (from the side, one complete ring and two half rings can be seen; the three points form a plane, which can be used as the orientation of the through-hole type spherical magnet a and the through-hole type spherical non-magnet b). [Coloring] The size of the rings is clearly visible, used for vertical release and observation of the state of falling in the transparent conductor tube 1, such as tilting, rotation, etc. Similarly, other types of solid spherical magnets a are also coated with colored rings 7 on the spherical surface in the opposite direction of the magnetization direction, and four different colored rings 7-1 are coated on the spherical surface in the same vertical diameter plane around the diameter. Solid spherical non-magnetic body b is coated with one colored ring 7 on the spherical surface, and four different colored rings 7-1 are evenly coated on the spherical surface in the same diameter plane around the diameter passing through the colored ring 7.During the demonstration, all five different colored rings face upwards. This is used to determine the alignment of the vertical axis of the center of the through-hole spherical magnet a, the through-hole spherical non-magnetic magnet b, and the solid spherical magnet a and the solid spherical non-magnetic magnet b with the central axis of the transparent conductor tube 1. Specifically, when the four different colored rings 7-1 (three of which form a plane) painted on the same plane on the spherical surface are parallel (coinciding) with the horizontal and vertical reference plates 6, and the gap around the spherical surface is the same as that in the transparent conductor tube 1 (i.e., the center of the sphere is on the central line of the transparent conductor tube 1), the magnets are released. This is in accordance with the instructions for the through-hole spherical magnet a, the through-hole spherical non-magnetic magnet b, and the solid spherical magnet b. Both body a and solid spherical non-magnetic body b are released in this manner to determine their orientation. The transparent conductor tube 1 (non-ferromagnetic material) is a cylindrical aluminum or copper tube with equally spaced smooth through holes punched in its side wall (indoor light allows the interior to be seen from the outside; if the indoor light is not clear, lights can be added to the opening and side of the transparent conductor tube 1). The through-hole type spherical magnet a and through-hole type spherical non-magnetic body b are of the same size and their diameters are smaller than the inner diameter of the transparent conductor tube 1 (generally about 2 mm). The interior of the transparent conductor tube 1 and the exterior surfaces of the through-hole type spherical magnet a and through-hole type spherical non-magnetic body b are smooth. Both are equipped with graduated transparent conductor tubes 1 (or a meter stick is fixed on the outer wall of the transparent conductor tube 1 along the generatrix direction, with the graduated side facing the observation direction for easy recording of the spatiotemporal situation of the through-hole spherical magnet a and the through-hole spherical non-magnetic body b using a video recorder). The two identical transparent conductor tubes 1 are vertically fixed on a vertical support 3, which is fixed on a horizontal tabletop 4. The bottom of the two identical transparent conductor tubes 1 is farther from the horizontal tabletop 4 than the diameter of the through-hole spherical magnet a and the through-hole spherical non-magnetic body b. There is a recess 5 on the horizontal tabletop 4 below the bottom of the two identical transparent conductor tubes 1 for the through-hole spherical magnet a. When the through-hole spherical non-magnetic object b falls onto the table, it is used for collection. The inner surface of the recess 5 is covered with sponge. A video recorder is fixed at a certain distance (determined according to the size of the device and the video clarity) directly opposite the two through-hole conductor tubes 1. The two vertical through-hole conductor tubes 1 fall clearly in the field of view of the video recorder lens. The video recorder is fixed about 20cm directly above the two vertical through-hole conductor tubes 1, with its lens facing the central axis of the through-hole conductor tubes 1. At the beginning of the experiment, the position, time and state of the through-hole spherical magnet a and the through-hole spherical non-magnetic object b falling are recorded (all subsequent experimental video recordings are recorded in this manner); during the experimental demonstration, ...

[0084] Experiment 1) Hold a through-hole spherical magnet a and a through-hole spherical non-magnetic body b with both hands respectively. With the lead block 2 facing downwards, release them simultaneously from two identical transparent conductor tubes 1 at the same height. At the moment of release, the vertical axis of the center of the through-hole spherical magnet a and the through-hole spherical non-magnetic body b coincides with the central axis of the transparent conductor tube 1. Observe the phenomenon.

[0085] Experiment 2) Then, the positions of the through-hole spherical magnet a and the through-hole spherical non-magnetic body b are interchanged and released into two identical transparent conductor tubes 1 respectively. The direction with lead block 2 is downward. At the moment of release, the vertical axis of the center of the through-hole spherical magnet a and the through-hole spherical non-magnetic body b coincides with the central axis of the transparent conductor tube 1. The experimental results show that the through-hole spherical magnet a descends more slowly than the through-hole spherical non-magnetic body b.

[0086] Experiment 3) As shown in Figure 1(c), cut off 1 / 4 of the lower 1 / 3 of the transparent conductor copper tube from the side in the observation direction and observe the effect of the through-hole spherical magnet a falling in the vertically processed transparent conductor tube 1. It is seen that the speed of the through-hole spherical magnet a in the cut section is faster than that in the uncut section. That is, there is also eddy current in the cut section of the transparent conductor tube 1, but it is smaller than that in the uncut section.

[0087] Experiment 4) Replace the through-hole spherical magnet a and the through-hole spherical non-magnetic body b with solid homogeneous spherical magnet a and solid homogeneous spherical non-magnetic body b of the same size. Replace the through-hole conductor tube 1 with a non-ferromagnetic material conductor tube 1 with no holes in the side wall. Cut off 1 / 4 of the side wall in the observation direction from the lower 1 / 3 of the tube. Repeat the operation process of Experiment 1) and Experiment 2). The main observation is to observe the motion state (trajectory, posture) of the solid homogeneous spherical magnet a and the solid homogeneous spherical non-magnetic body b falling in the vertical non-ferromagnetic material conductor tube 1 with no holes in the side wall.

[0088] Experiment 5) Further, replace the materials of the two identical (same structure, same size) transparent conductor tubes 1 with (collectively referred to as transparent tube 1): columnar transparent tubes 1 of the same size and structure made of transparent organic plastic, aluminum, copper, iron, and superconducting materials. Repeat the operation process of Experiment 1) and Experiment 2). Hold the through-hole spherical magnet a and the through-hole spherical non-magnetic body b with both hands, and release them at the same height at the tube opening with the lead block facing downwards. Release them after the vertical axis of the center of the through-hole spherical magnet a and the through-hole spherical non-magnetic body b coincides with the central axis of the transparent tube 1 (or use the lower 1 / 3 of the transparent tube 1 to cut 1 / 4 of the side view in the observation direction). Record the position, time and falling state of the through-hole spherical magnet a and the through-hole spherical non-magnetic body b with a fixed video recorder. You will see:

[0089] Demonstration Experiment Phenomena: (1) When the transparent organic plastic tube 1 is in the case of the through-hole type spherical magnet a and the through-hole type spherical non-magnetic body b, their falling speeds tend to be the same; (2) When the transparent tube 1 is made of aluminum, the through-hole type spherical magnet a falls slower than the through-hole type spherical non-magnetic body b; (3) When the transparent tube 1 is made of copper, the through-hole type spherical magnet a falls slower than the through-hole type spherical non-magnetic body b (slower than the case of the aluminum tube); (4) When the transparent tube 1 is made of iron, the through-hole type spherical magnet a falls slower than the through-hole type spherical non-magnetic body b, and may also be attracted. (5) If the permeable tube 1 is in a superconducting state under the condition of superconducting material, the through-hole spherical magnet a is suspended at the tube port of the permeable tube 1 (the superconducting tube has complete diamagnetism and the descent speed tends to zero) or the through-hole spherical magnet a is changed to a through-hole spherical superconducting ball and is in a superconducting state, while the permeable superconducting material tube is changed to a strong magnet tube (magnetized along the axis of the magnet tube, the through-hole spherical superconducting ball has complete diamagnetism and the descent speed tends to zero), and the through-hole spherical superconducting ball will be suspended at the tube port;

[0090] Experiment 6) In a through-hole spherical non-magnetic body b (or a solid spherical non-magnetic body b whose center of mass coincides with the center of the sphere), a through-hole spherical magnet a (or a solid spherical magnet a uniformly magnetized with its center of mass coincides with the center of the sphere), and a through-hole spherical magnet a (or a solid spherical magnet a uniformly magnetized with its center of mass coincides with the center of the sphere), the magnetization vector of the solid spherical magnet a (through-hole spherical magnet a) is M0 (or the magnetization direction of the magnet surface). When B is constant (e.g., B = 0.1 Tesla, 0.5 Tesla), the radius of the through-hole spherical magnet and the solid spherical magnet is R0 (e.g., 20 mm), the wall thickness of the through-hole non-ferromagnetic material conductor tube 1 (or the non-ferromagnetic material conductor tube 1 with no side holes) is b (2 mm), and the resistivity of the conductor tube 1 (non-ferromagnetic) is ρ (e.g., commonly used aluminum or copper materials) remains constant, the length of the through-hole conductor tube (or the conductor tube with no side holes) is constant (e.g., 1 meter high). [Or, as shown in Figures 1(c) and 1(d), the length of the transparent conductor tube (or the conductor tube without side holes) is fixed (e.g., 1 meter high), and the lower 1 / 3 of the transparent conductor tube (or conductor tube) is cut off from the side in the observation direction by 1 / 4 of the side], that is, under the condition that other conditions remain unchanged, the inner radii r of 10 sizes (20 in total, 2 of each size, that is: for each type, such as the transparent conductor tube 1 of the same material, a total of 20, 2 of each size) of the transparent conductor tube 1 (or the conductor tube 1 without side holes) of the same material are R0(1+0.1), R0(1+0.2), R0(1+0.3), R0(1+0.4), R0(1+0.5), R0(1+0.6), R0(1+0.7), R0(1+0.8), R0(1+0.9), R0(1+1), where conductor tube 1 refers to the abbreviation of non-ferromagnetic material conductor tube 1;

[0091] Repeat the procedures of experiments 1) and 2). Hold a through-hole spherical magnet a and a through-hole spherical non-magnetic body b, or two solid spherical magnets a and b of the same size, in each hand. Release the through-hole spherical magnet a (or solid spherical magnet a) simultaneously at the same height, with the magnetized direction facing downwards. That is, release the through-hole spherical non-magnetic body b and the through-hole spherical magnet a, or the solid spherical magnet a and solid spherical non-magnetic body b, after their central vertical axes coincide with the central axis of the through-hole conductor tube 1 or the conductor tube 1 without side holes. Record the position, time, and state of the through-hole spherical magnet a and the through-hole spherical non-magnetic body b, or the two solid spherical magnets a and solid spherical non-magnetic bodies b of the same size, using a fixed video recorder. Measure the mass m of the through-hole spherical magnet a and the mass m1 of the spherical non-magnetic body b using a balance.

[0092] According to the magnetic resistance formula or

[0093] Position-time equation of non-magnetic body

[0094] Position-time equation of a magnet Data processing and analysis;

[0095] Experiment 7) In a perforated spherical nonmagnetic body b (or a solid spherical nonmagnetic body b with its center of mass coinciding with the center of the sphere), a perforated spherical magnet a (or a solid spherical magnet a with its center of mass coinciding with the center of the sphere and uniformly magnetized), a perforated spherical magnet a (or a solid spherical magnet a with its center of mass coinciding with the center of the sphere and uniformly magnetized), the magnetization vector is M0 (or the magnet surface B in the magnetization direction is constant, such as B = 0.1 Tesla, 0.5 Tesla), the radius of the perforated spherical nonmagnetic body and the solid magnet is R0 (such as 20 mm), the inner radius of the transparent non-ferromagnetic material conductor tube 1 (or the non-ferromagnetic material conductor tube 1 with no holes in the sidewalls) is r, and the resistivity of the conductor tube 1 (non-ferromagnetic material) is constant at ρ (such as commonly used aluminum or copper materials), the perforated conductor... The length of the tube (or the conductor tube without sidewall holes) is fixed (e.g., 1 meter high) [or as shown in Figures 1(c) and 1(d), the length of the through conductor tube (or the conductor tube without sidewall holes) is fixed (e.g., 1 meter high), and the lower 1 / 3 of the through conductor tube (or conductor tube) is cut off from the side in the observation direction by 1 / 4 of the side], that is, under the condition that other conditions remain unchanged, the through conductor tube 1 of the same material or the conductor tube 1 with sidewall holes is replaced, and 10 sizes of each type of tube are made, with 2 tubes of each size (e.g., 20 through conductor tubes 1 of the same material, 2 of each size), and the tube wall thickness b is 1mm, 1.5mm, 2mm, 2.5mm, 3mm, 3.5mm, 4mm, 4.5mm, 5mm, 5.5mm respectively;

[0096] Repeat the procedures of experiments 1) and 2). Hold a through-hole spherical magnet a and a through-hole spherical non-magnetic body b, or two solid spherical magnets a and b of the same size, in each hand. Release the through-hole spherical magnet a (or solid spherical magnet a) simultaneously at the same height, with the magnetized direction facing downwards. That is, release the through-hole spherical non-magnetic body b and the through-hole spherical magnet a, or the solid spherical magnet a and solid spherical non-magnetic body b, when their central vertical axes coincide with the central axis of the through-hole conductor tube 1 or the conductor tube 1 without side holes. Record the position, time, and state of the through-hole spherical magnet a and the through-hole spherical non-magnetic body b, or the two solid spherical magnets a and solid spherical non-magnetic bodies b of the same size, using a fixed video recorder. Measure the mass m of the through-hole spherical magnet a and the mass m1 of the spherical non-magnetic body b using a balance.

[0097] According to the magnetic resistance formula or Position-time equation of non-magnetic body Position-time equation of a magnet 1) Data processing and analysis.

[0098] Experiment 8) In a through-hole spherical non-magnetic body b (or a solid spherical non-magnetic body b whose center of mass coincides with the center of the sphere), a through-hole spherical magnet a (or a solid spherical magnet a uniformly magnetized with its center of mass coincides with the center of the sphere), and a through-hole spherical magnet a (or a solid spherical magnet a uniformly magnetized with its center of mass coincides with the center of the sphere), the magnetization vector of the magnet is M0 (or the magnetization direction of the magnet surface B is constant, such as B = 0.1 Tesla, 0. When the inner radius r, wall thickness b, and resistivity ρ (such as commonly used aluminum or copper materials) of the permeable conductor tube (1) or the non-ferromagnetic conductor tube (1) (with no side holes) remain constant, and the length of the permeable non-ferromagnetic material conductor tube 1 (or the non-ferromagnetic material conductor tube 1 with no side holes) is constant (such as 1 meter high) [or as shown in Figure 1(c) and Figure 1(d) permeable conductor tube ( Or, if the length of a conductor tube (without side holes) is fixed (e.g., 1 meter high), and the lower 1 / 3 of the conductor tube (or the conductor tube) is cut off at 1 / 4 of its side in the observation direction, then, under the condition that other conditions remain unchanged, the radius R0 of the through-hole type spherical magnet a and the through-hole type spherical non-magnetic body b (solid spherical magnet a and solid spherical non-magnetic body b) is changed, and the radius R0 of the sphere is changed, and 10 sizes of each type of sphere are made (e.g., through-hole type spherical magnet a and through-hole type spherical non-magnetic body b). There are 20 spherical nonmagnetic bodies (b in total), with R0 values ​​of r(1-0.1), r(1-0.15), r(1-0.2), r(1-0.25), r(1-0.3), r(1-0.35), r(1-0.4), r(1-0.45), r(1-0.5), and r(1-0.55); where r is the inner radius of the transparent non-ferromagnetic material conductor tube 1 (or the non-ferromagnetic material conductor tube 1 with no pores in the sidewalls);

[0099] Repeat the procedures of Experiments 1) and 2). Hold the through-hole spherical magnet a and the through-hole spherical non-magnetic magnet b, or two solid spherical magnets a and b of the same size, in each hand respectively. Release the through-hole spherical magnet a (or solid spherical magnet a) simultaneously from the same height, with the magnetized direction facing downwards. That is, the vertical axis of the center of the through-hole spherical non-magnetic magnet b and the through-hole spherical magnet a, or the solid spherical magnet a and the solid spherical non-magnetic magnet b, should be aligned with the through conductor tube. 1. Or, release the conductor tube 1 (either a non-ferromagnetic material conductor tube 1 or a non-ferromagnetic material conductor tube 1 with no side holes) after its central axis is aligned; record the positions of the through-hole spherical magnet a and the through-hole spherical non-magnetic body b, or the positions, times, and states of two solid spherical magnets a and solid spherical non-magnetic bodies b of the same size, using a fixed video recorder; measure the mass m of the through-hole spherical magnet a and the mass m1 of the spherical non-magnetic body b using a balance, and apply the magnetic resistance formula... or Position-time equation of non-magnetic body Position-time equation of a magnet Data processing and analysis.

[0100] Experiment 9) In a through-hole spherical non-magnetic body b (or a solid spherical non-magnetic body b whose center of mass coincides with the center of the sphere), a through-hole spherical magnet a (or a solid spherical magnet a uniformly magnetized with its center of mass coincides with the center of the sphere), and a through-hole spherical magnet a (or a solid spherical magnet a uniformly magnetized with its center of mass coincides with the center of the sphere), the magnetization vector of the magnet is M0 (or the magnetization direction of the magnet surface B is constant, such as B = 0.1 Tesla). 0.5 Tesla), a through-hole spherical magnet or a solid spherical magnet with radius R0, an inner radius r of a non-ferromagnetic material conductor tube 1 (or a non-ferromagnetic material conductor tube 1 without sidewall holes), a tube wall thickness b, and a resistivity ρ (such as commonly used aluminum or copper materials) of the conductor tube 1 (non-ferromagnetic) remain constant, and the length of the through-hole conductor tube 1 (or the conductor tube 1 without sidewall holes) is constant (such as 1 meter high) [or as shown in Figure 1(c) and Figure 1(d)]. When the length of a through-hole spherical magnet a (or a conductor tube without side holes) is fixed (e.g., 1 meter high), and the lower 1 / 3 of the through-hole spherical magnet a is cut off from the side in the observation direction at 1 / 4 of its side length, the magnetization intensity M0 of the through-hole spherical magnet a (or a solid spherical magnet a with its center of mass coinciding with the center of the sphere and uniformly magnetized) is changed. That is, under the condition that other conditions remain unchanged, the magnetization intensity M0 of the through-hole spherical magnet a and the through-hole spherical non-magnetic magnet b, or two of the same size, is changed. Ten solid spherical magnets a and ten solid spherical non-magnetic magnets b of the same size are made. The magnetization intensity M0 of the magnets decreases sequentially as follows: M0(1-0.1), M0(1-0.15), M0(1-0.2), M0(1-0.25), M0(1-0.3), M0(1-0.35), M0(1-0.4), M0(1-0.45), M0(1-0.5), and M0(1-0.55).

[0101] Repeat the procedures of experiments 1) and 2). Hold a through-hole spherical magnet a and a through-hole spherical non-magnetic body b, or two solid spherical magnets a and b of the same size, in each hand. Release the through-hole spherical magnet a (or solid spherical magnet a) simultaneously at the same height, with the magnetized direction facing downwards. That is, release the through-hole spherical non-magnetic body b and the through-hole spherical magnet a, or the solid spherical magnet a and solid spherical non-magnetic body b, when their central vertical axes coincide with the central axis of the through-hole conductor tube 1 or the conductor tube 1 without side holes. Record the position, time, and state of the through-hole spherical magnet a and the through-hole spherical non-magnetic body b, or the two solid spherical magnets a and solid spherical non-magnetic bodies b of the same size, using a fixed video recorder. Measure the mass m of the through-hole spherical magnet a and the mass m1 of the spherical non-magnetic body b using a balance.

[0102] According to the magnetic resistance formula or Position-time equation of non-magnetic body Position-time equation of a magnet Data processing and analysis.

[0103] Data processing and analysis can yield a wealth of meaningful information, such as combining experimental data with the position-time equations of non-magnetic bodies. Position-time equations of magnets The relationships between the air drag coefficient k1 and the magnetic drag coefficient k and various physical quantities such as M0, R0, b, and r are obtained respectively. (where the coefficients α, β, γ, δ, ∈ are obtained through data fitting) and together with Comparison (which pertains to data processing and will not be elaborated upon in this patent specification).

[0104] Experiment 10) Small magnetic ring magnet position recording device, as shown in the attached document. Figure 6 For a conductor tube with non-ferromagnetic material and non-porous sidewalls, where the position and time relationship between the through-hole spherical magnet a and the through-hole spherical non-magnetic magnet b cannot be directly read visually from the outside (the video recorder is outside the tube), a magnetic position recording device can be fixed along the generatrix on the outside of the non-ferromagnetic material conductor tube with non-porous sidewalls. Magnetic powder or small magnetic rings can be used as position markers. Taking the small magnetic ring 8 as an example, a smooth non-ferromagnetic material straight rod 9 with graduations is fitted with a matching small magnetic ring 8 (whose volume and mass are much smaller than that of the through-hole spherical magnet a). The small magnetic ring 8 moves along with the position of the through-hole spherical magnet a without affecting the fall of the through-hole spherical magnet a (the volume and mass of the small magnetic ring 8 are much smaller than those of the through-hole spherical magnet a, so its impact on the through-hole spherical magnet a during the fall is weak; the deviation of the through-hole spherical magnet a from vertical during the short fall of about 1 meter can be ignored (this method can also be used to determine the position of a through-hole spherical non-magnetic body b made of ferromagnetic material). In this way, by recording the position of the small magnetic ring 8 (through-hole spherical magnet a) with a video recorder, the position and time data of the through-hole spherical magnet a can be determined.

[0105] Note: Under the condition that other parameters remain unchanged, the magnetic permeability between the sphere and the tube can be changed from the vacuum permeability μ0 to other materials, such as the permeability μ of mercury vapor (because mercury vapor is toxic, it must be carried out under safe conditions), to design demonstration experiments. The changes in physical parameters mentioned in this patent, such as the wall thickness b of the transparent non-ferromagnetic material conductor tube 1 (or the conductor tube 1 with no sidewall pores) being 1mm, 1.5mm, 2mm, 2.5mm, 3mm, 3.5mm, 4mm, 4.5mm, 5mm, and 5.5mm respectively; and the inner radius r being R0(1+0.1), R0(1+0.2), R0(1+0.3), R0(1+0.4), R0(1+0.5), R0(1+0.6), R0(1+0.7), R0(1+0.8), R0(1+0.9), and R0(1+1) respectively; all refer to experimental studies under the condition that other parameters remain unchanged (controlled variable method). In the experiment, release refers to the release after the central vertical axis of the through-hole spherical non-magnetic body and the through-hole spherical magnet (or the solid spherical magnet and the solid spherical non-magnetic body) coincides with the central axis of the permeable tube 1 (or the conductor tube 1 with no sidewall holes); the permeable tube 1 mentioned in this patent includes: a permeable non-ferromagnetic material conductor tube (e.g., copper tube, aluminum tube), a permeable non-conductor tube (e.g., transparent plastic tube), a permeable ferromagnetic material conductor tube (e.g., iron material tube), and a permeable superconducting material tube; unless otherwise specified in this patent specification, the permeable conductor tube 1 or conductor tube 1 refers to a conductor tube made of non-ferromagnetic material; this patent was commissioned to be written by Liang Faku, one of the inventors.

Claims

1. A method for demonstrating eddy currents in a magnet and a conductor tube with variable geometric parameters, the device mainly consisting of a through-hole spherical magnet a, a through-hole spherical non-magnetic body b, two identical through-conductor tubes, a vertical support, a horizontal tabletop, and horizontal and vertical reference plates, characterized in that: The through-hole type spherical magnet a is a sphere made of hard magnetic material, with through holes passing through the center of the sphere sintered at equal intervals on its surface. A lead block is then inserted into one of the holes for fixation, the size of which matches the size of the lead block. Magnetization is performed on the magnetizing device along the direction of the lead block passing through the center of the sphere. The through-hole type spherical non-magnetic magnet b is a sphere of the same size as the through-hole type spherical magnet a, made of alloy or aluminum material. Through holes passing through the center of the sphere are punctured at equal intervals on its surface, with the same diameter, spacing, and number of holes as the through-hole type spherical magnet a. The horizontal and vertical reference plates are fixed to a vertical support by straight rods. The straight reference plate is a thin metal plate; the through-hole type spherical magnet a and the through-hole type spherical non-magnetic body b have five different colored rings painted on the opposite surface of the lead block using a marker pen. One colored ring is painted on the edge of the through-hole with the same diameter as the lead block, and the other four colored rings are evenly distributed in the same plane and perpendicular to the spherical surface passing through the diameter of the lead block; the transparent conductor tube is a transparent non-ferromagnetic material conductor tube, which is a columnar aluminum tube or a columnar copper tube with equally spaced smooth through holes punched in its side wall; the through-hole type spherical magnet a and the through-hole type spherical non-magnetic body b... b is of the same structure and size, but with a diameter smaller than the inner diameter of the transparent conductor tube. The interior of the transparent conductor tube and the exterior surfaces of both the through-hole spherical magnet a and the through-hole spherical non-magnet b are smooth. The two identical transparent conductor tubes are homogeneous cylindrical straight tubes with graduations, the graduated side facing the observation direction for easy recording of the spatiotemporal state of the through-hole spherical magnet a and the through-hole spherical non-magnet b using a video recorder. The transparent conductor tubes are vertically fixed to a vertical support, which is fixed to a horizontal tabletop. The bottom of the two identical transparent conductor tubes is further from the horizontal tabletop than the distance between the through-hole spherical magnet a and the through-hole spherical non-magnet b. The diameter of non-magnetic object b is shown in the image. A recess is located on the horizontal tabletop at the bottom of two identical transparent conductive tubes. This recess is used to collect the through-hole spherical magnet a and the through-hole spherical non-magnetic object b as they fall onto the tabletop. Sponge is pasted onto the inner surface of the recess. A video recorder is fixed at a certain distance directly opposite the two vertical tubes, ensuring the two tubes are clearly visible in the video recorder's lens field of view. The video recorder is also fixed approximately 20cm directly above the two vertical tubes, with its lens facing the central axis of the transparent conductive tube. The experiment begins by recording the position, time, and state of the through-hole spherical magnet a and the through-hole spherical non-magnetic object b as they fall. Experimental demonstration: Experiment 1) Hold a through-hole spherical magnet a and a through-hole spherical non-magnetic body b with both hands respectively, with the lead block facing down and at the same height, and release them from two identical transparent conductor tubes respectively. At the moment of release, the vertical axis of the center of the through-hole spherical magnet a and the through-hole spherical non-magnetic body b coincides with the central axis of the transparent conductor tube. Observe the phenomenon. Experiment 2) Then, the through-hole type spherical magnet a and the through-hole type spherical non-magnetic body b demonstrated in Experiment 1) are interchanged and released simultaneously in two identical transparent conductor tubes. The direction with lead block 2 is facing downwards. At the moment of release, the vertical axis of the center of the through-hole type spherical magnet a and the through-hole type spherical non-magnetic body b coincides with the central axis of the transparent conductor tube. Observe the phenomenon. The experimental results show that the through-hole type spherical magnet a descends more slowly than the through-hole type spherical non-magnetic body b. Experiment 3) Cut off 1 / 4 of the lower 1 / 3 of the transparent conductor copper tube from the side in the observation direction and observe the effect of the through-hole spherical magnet a falling in the vertically processed transparent conductor tube. It is seen that the speed of the through-hole spherical magnet a in the cut section is faster than that in the uncut section. That is, there is also eddy current in the cut section of the transparent conductor tube, but it is smaller than that in the uncut section. Experiment 4) Replace the through-hole spherical magnet a and the through-hole spherical non-magnetic body b with solid homogeneous spherical magnet a and solid homogeneous spherical non-magnetic body b of the same size. Replace the transparent conductor tube with a non-ferromagnetic material conductor tube with no holes in the side wall. Cut off 1 / 4 of the side wall from the lower 1 / 3 of the tube in the observation direction. Repeat the operation process of Experiment 1) and Experiment 2). The main observation is the motion state of the spherical magnet a and the solid homogeneous spherical non-magnetic body b falling in the vertical non-ferromagnetic material conductor tube with no holes in the side wall. Experiment 5) Replace the materials of the two identical transparent conductive tubes with: transparent organic plastic, aluminum, copper, iron, and superconducting material, respectively. That is, the transparent tubes are homogeneous cylindrical straight tubes made of transparent organic plastic, aluminum, copper, iron, and superconducting material, respectively. The transparent tubes are the same size, wall thickness, and structure. Smooth through-holes of the same size and evenly spaced are drilled into the sidewalls of the tubes. The transparent tubes include: transparent non-ferromagnetic material conductive tubes, transparent non-conducting tubes, transparent ferromagnetic material conductive tubes, and transparent superconducting material tubes. Repeat Experiments 1) and 2), and compare the eddy current effects of the transparent tubes made of different materials. Hold a through-hole spherical magnet a and a through-hole spherical non-magnetic magnet b in each hand, and release them simultaneously from the same height with the lead block facing downwards. The following will be observed: (1) In the case of a transparent organic plastic tube, the falling speed of the through-hole spherical magnet a and the through-hole spherical non-magnetic body b tends to be the same; (2) In the case of aluminum, the through-hole spherical magnet a falls slower than the through-hole spherical non-magnetic body b; (3) In the case of copper, the through-hole spherical magnet a falls slower than the through-hole spherical non-magnetic body b and is slower than the case of aluminum tube; (4) In the case of iron tube, the through-hole spherical magnet a falls slower than the through-hole spherical non-magnetic body b and may be attracted to the tube. (5) In the case of superconducting materials, if it is made to be in a superconducting state, the through-hole spherical magnet a is suspended at the tube port, or the through-hole spherical magnet a is replaced with a through-hole spherical superconductor ball of the same size and is in a superconducting state, while the through-hole superconducting material tube is replaced with a strong magnet tube, the magnetic poles of the strong magnet tube are parallel to the central axis of the tube, the through-hole spherical superconductor ball has complete diamagnetism, the falling speed tends to zero, and the through-hole spherical superconductor ball will be suspended at the tube port; Experiment 6) Under the condition that other conditions remain unchanged, make 10 scales of a transparent conductor tube or a conductor tube with no holes in the sidewalls, each scale with two inner radii r of R0(1+0.1), R0(1+0.2), R0(1+0.3), R0(1+0.4), R0(1+0.5), R0(1+0.6), R0(1+0.7), R0(1+0.8), R0(1+0.9), and R0(1+1). Repeat the operation process of Experiment 1) and Experiment 2). Hold the through-hole spherical magnet a and the through-hole spherical non-magnetic body b in each hand, or two solid spherical magnets a and b of the same size. Release them simultaneously at the same height with the magnetization direction facing downwards. That is, release them after the vertical axis of the through-hole spherical non-magnetic body b and the through-hole spherical magnet a or the solid spherical magnet a and the solid spherical non-magnetic body b coincides with the central axis of the through conductor tube (1) or the conductor tube (1) without side holes. Record the position, time and state of the through-hole spherical magnet a and the through-hole spherical non-magnetic body b with a fixed video recorder. Measure the mass of the through-hole spherical magnet a with a balance. Experiment 7) Under the condition that other conditions remain unchanged, for each type of tube, 10 sizes of transparent conductor tubes or conductor tubes with no sidewall holes are made, and 2 tubes of each size are made, with tube wall thickness b of 1mm, 1.5mm, 2mm, 2.5mm, 3mm, 3.5mm, 4mm, 4.5mm, 5mm and 5.5mm respectively. Repeat the operation process of Experiment 1) and Experiment 2). Hold the through-hole spherical magnet a and the through-hole spherical non-magnetic body b or the solid spherical magnet a and the solid spherical non-magnetic body b in each hand. Release them at the same height with the magnetization direction facing downwards. That is, release them after the central vertical axis of the through-hole spherical non-magnetic body b and the through-hole spherical magnet a or the solid spherical magnet a and the solid spherical non-magnetic body b coincides with the central axis of the through conductor tube (1) or the conductor tube (1) with no holes in the sidewalls. Record the position, time and state of the through-hole spherical magnet a and the through-hole spherical non-magnetic body b with a fixed video recorder. Measured data combined with the formula magnetic resistance formula or magnetic drag coefficient Non-magnetic position space-time motion equations Equations of position, space, and time of magnet analyze; Experiment 8) In a through-hole type spherical non-magnetic body b, or a solid spherical non-magnetic body b whose center of mass coincides with the center of the sphere, a through-hole type spherical magnet a, or a solid spherical magnet a uniformly magnetized with its center of mass coincides with the center of the sphere, or a through-hole type spherical magnet a, or a solid spherical magnet a uniformly magnetized with its center of mass coincides with the center of the sphere, the magnetization vector of the magnet is M0, the inner radius r of the through conductor tube (1) or the conductor tube (1) without side holes, the tube wall thickness is b, and the conductor tube (1) When the resistivity ρ remains constant, and when the length of the through-conductor tube (1) or the conductor tube (1) without sidewall holes is constant, the radius R0 of the sphere is changed, and 10 sizes of each type of sphere are made, with R0 being r(1-0.1), r(1-0.15), r(1-0.2), r(1-0.25), r(1-0.3), r(1-0.35), r(1-0.4), r(1-0.45), r(1-0.5), and r(1-0.55); Repeat the procedures of experiments 1) and 2). Hold the through-hole spherical magnet a and the through-hole spherical non-magnetic body b, or two solid spherical magnets a and b of the same size, respectively, with the magnetized direction of the through-hole spherical magnet a (solid spherical magnet a) facing downwards and released at the same height. That is, release the through-hole spherical non-magnetic body b and the through-hole spherical magnet a, or the solid spherical magnet a and the solid spherical non-magnetic body b, after their central vertical axis coincides with the central axis of the through-hole conductor tube (1) or the conductor tube (1) without side holes. Record the position, time and state of the through-hole spherical magnet a and the through-hole spherical non-magnetic body b, or the two solid spherical magnets a and the solid spherical non-magnetic body b of the same size, using a fixed video recorder. Measure the mass m of the through-hole spherical magnet a and the mass m1 of the spherical non-magnetic body b using a balance. According to the magnetic resistance formula or magnetic drag coefficient Position-time equation of non-magnetic body Magnet position-time equation Data processing and analysis; Experiment 9) Under the condition that other conditions remain unchanged, 10 through-hole spherical magnets a and through-hole spherical non-magnets b of the same size are made respectively. The magnetization intensity M0 of the magnets decreases in sequence as follows: M0(1-0.1), M0(1-0.15), M0(1-0.2), M0(1-0.25), M0(1-0.3), M0(1-0.35), M0(1-0.4), M0(1-0.45), M0(1-0.5), M0(1-0.55). Repeat the procedures of experiments 1) and 2). Hold the through-hole spherical magnet a and the through-hole spherical non-magnetic body b in each hand. Release the through-hole spherical magnet a with the magnetized direction facing downwards at the same height. That is, release the through-hole spherical non-magnetic body b and the through-hole spherical magnet a after their central vertical axes coincide with the central axis of the through-hole conductor tube (1) or the conductor tube (1) with no holes in the sidewalls. Record the position, time and state of the through-hole spherical magnet a and the through-hole spherical non-magnetic body b with a fixed video recorder. Measure the mass m of the through-hole spherical magnet a and the mass m1 of the spherical non-magnetic body b with a balance. According to the magnetic resistance formula or Position-time equation of non-magnetic body Position-time equation of a magnet For data processing and analysis, Where: M0 is the magnetization vector of spherical magnet a, R0 is the radius of spherical magnet a, b is the thickness of conductor tube (1), r is the inner radius of conductor tube (1), ρ is the resistivity of conductor tube (1), μ0 is the permeability of vacuum, v is the velocity of the magnet, k1 is the air resistance coefficient, k is the magnetic resistance coefficient, and m1 and m are the masses of spherical non-magnetic body and spherical magnet, respectively.

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