In this study, we derived several formulas for the currents induced in a circular loop by a magnet connected to a spring-based simple harmonic oscillation system. In addition, we conducted an experiment for measuring the induced currents and compared the results with the theoretical prediction. It was confirmed that the prediction from the derived formulas fits well with experimental results. Via derived formulas and a simple experiment, Faraday’s Law and Lenz’s Law could be easily explained.

In this study, two types of approximate analytic functions for the off-axis magnetic field B ⃗ r , θ of a circular loop and a finite-length solenoid are presented. The derived analytic functions reduce to a well-known magnetic field formula with respect to the vertical axis of the circular loop and the solenoid when θ = 0 . In addition, we investigated two types of B ⃗ r , θ within the approximate conditions through a simulation performed using Wolfram Mathematica. The derived analytic functions can be used to determine the magnetic field B ⃗ r , θ at arbitrary points with large r and small θ around a circular loop and a solenoid. They are helpful for investigating the electromagnetic induction that can be attributed to a magnet swinging over a coil or a solenoid.

In this study, formulae for the waveform of an induced current, I(t), generated when a magnet traverses along a rectangular coil with a narrow width were theoretically obtained considering the relative motion of the magnet and coil. Consequently, an experiment was performed under experimental conditions that matched the formulas, and the results obtained were compared with the theoretical predictions. The dependence of I(t) on the initial angle ϕ 0 of the magnet pendulum and the width w of the rectangular coil was found to be consistent with the theoretical prediction. Thus, the formulae obtained in this study are expected to be useful in addressing temporal variations in the waveform of the induced current produced by a magnet moving in a polar coordinate space.

In this study, we derived formulas for the current waveforms induced by a magnet oscillating at arbitrary positions on the axis of a solenoid. We also conducted an experiment for measuring the currents induced in a solenoid by a magnet oscillating in the inner or outer region of a solenoid and compared the results with the theoretical predictions. It was confirmed that the magnitude and shape of waveforms of induced currents that were obtained from the derived formulas fit well with experimental results. In addition, the magnetic drag force exerted on the magnet by the induced current is formulated and compared with the prediction estimated by the attenuation coefficient and velocity.