Forces between permanent magnets: experiments and model

Abstract

This work describes a very simple, low-cost experimental setup designed for measuring the force between permanent magnets. The experiment consists of placing one of the magnets on a balance, attaching the other magnet to a vertical height gauge, aligning carefully both magnets and measuring the load on the balance as a function of the gauge reading. A theoretical model is proposed to compute the force, assuming uniform magnetisation and based on laws and techniques accessible to undergraduate students. A comparison between the model and the experimental results is made, and good agreement is found at all distances investigated. In particular, it is also found that the force behaves as r−4 at large distances, as expected.

Research on a novel magnetic tilt sensor designed using Hall elements and ferrofluid

“…There are several studies in which approximate solutions of (1) were obtained. In these studies, it was shown that the magnetic field is proportional to the power law of distance as z −3 and the magnetic force is proportional to z −4 when a ≫ z [12,13]. Also, there are several articles where both the field and the force between the two magnets are examined theoretically by using relatively complex mathematical solutions [12,14].…”

“…In these studies, it was shown that the magnetic field is proportional to the power law of distance as z −3 and the magnetic force is proportional to z −4 when a ≫ z [12,13]. Also, there are several articles where both the field and the force between the two magnets are examined theoretically by using relatively complex mathematical solutions [12,14]. For the sake of simplicity, a practical expression of force and magnetic field were calculated analytically with some assumptions and approximations in the following part.…”

“…It was found from force expression (6) that ∆z is an approximate linear function of sin α . In this case, (12) and (13) will be as follows by using (6)…”

Determination of magnon mass of neodymium magnet by temperature dependence of spontaneous magnetization

“…The physics of magnetism is always an important part of the physics education in high school, college and university level for undergraduate laboratories. Let us mention some recent topics: 1) magnetic bridge sensor for observation of superconducting-tonormal phase transition in a high-temperature superconductor and the Curie point of a ferromagnet [1], 2) using the smartphone magnetic field sensor or magnetometer let to popularization which can be used by every student even in home experiments [2], 3) magnetic sensor in a smartphone as an alternate to the relatively expensive magnetic sensor probe for accurate measurements [3], 4) with additional efforts a compact magnetometer consisting of two Hall effect-based sensors can be built which allows measuring the magnetic response of the iron oxide microparticle sample [4] 5) mechanical set-ups require much more attention, but study of torque oscillations of a rotational motion in Helmholtz coils gives a reliable method for the determination of magnetization of a permanent magnet [5] 6) in this direction neodymium disc magnet play important role to enhance knowledge of the physics of magnetism and especially to estimate magnetic dipole moment [6] 7) simple, low-cost experimental setup designed for measuring the force between permanent magnets are very appropriate for undergraduate students [7] 8) magnetic measurements are very appropriate if students have complete autonomy to develop their experimental set-up using open-source low-cost equipment including Arduino microcontrollers and compatible sensors [8], 9) the theoretical studies of Ising-spin model [9] completes the culture of education in physics of magnetism.…”

Interaction Forces and Torques between Two Perpendicular Magnetic Tubes

“…For cylindrical permanent magnets, the magnetic force between two coaxial/parallel magnets has been calculated assuming uniform magnetization and studied by magnetostatic interaction energy [20], Kelvin's formula [21], Ampere's formula [22], and Lorentzian model [23], respectively. The analytical expression of the attractive force between two arrays of cylindrical permanent magnets was derived from the derivative of the total magnetostatic interaction energy with respect to the axial coordinate [24,25].…”