Weber-Ritz & Faraday-Maxwell Formulae: Induction Experiment Test
Ray T. Smith
In order to return to the origins of the theories of electromagnetic induction, a comparison is made between the theories of Weber-Ritz (W-R) and Faraday-Maxwell (F-M) for the case of a coil carrying a constant current and moving with constant velocity through a stationary coil. The approach is then in terms of clearly defined current elements, which in one case (W-R) involves direct action/emission between the elements, and the other (F M) involves action via magnetic fields. The theoretical approach is simplified by considering thin, single-circle current loops a given distance apart, which then only requires a single integration around the loops. The induced voltage is calculated using the principle of superposition and treating each coil as a stack of current loops. The experimental arrangement is made as simple as possible; the current-carrying coil is dropped under gravity via a central guide through the stationary coil. The induced voltage pulses are recorded on a digital storage oscilloscope linked to a printer.
The Numerical computations in the case of single loops indicate that the Weber-Ritz and Faraday-Maxwell theories agree to better than 0.1%, provided that in the latter case the calculation uses the radial magnetic field (given by magneto-statics) and the simple flux cutting rule. Agreement between experiment and theory proved to be well within the limits of experimental error, and showed greater consistency with more turns on the coils. Finally some comments are offered regarding the validity of the comparison, the relative merits of W-R & F-M theories, and the Aharonov Bohm effect in relation to classical electrodynamics.
