- #1

- 139

- 5

The near-range magnetic field ##\vec{B}## of a point charge ##q## at distance ##\vec{r}##, moving at a non-relativistic velocity ##\vec{v}##, is given by

$$\vec{B}=\frac{q}{4\pi\epsilon_0c^2}\frac{\vec{v}\times\hat{r}}{r^2}.$$

Faraday's law of induction for the induced EMF ##V_c## in a coil, with area ##A## and turns ##N##, due to a changing magnetic field strength ##dB/dt## through its center is given by

$$V_c=-NA\frac{dB}{dt}.$$

In scenario ##A## the charge ##q## is falling downwards due to the gravitational force ##mg## and the coil is fixed at a distance ##r## so that the induced voltage ##V_c## measured by the coil is

$$V_c = - \frac{1}{4\pi\epsilon_0c^2}\frac{N\ A\ q\ g}{r^2}.$$

But according to the equivalence principle this is exactly the same as scenario ##B## in which the charge ##q## is fixed and the coil at distance ##r## is accelerating upwards with acceleration ##g##.

In scenario ##B## is there still an induced voltage ##V_c## across the moving coil?

P.S. I think one could actually do an experiment like this but one would replace the moving charge with a moving parallel plate capacitor which would produce a dipole magnetic field.