E.5.10 Reality of the Vector Potential

In the ideal case the magnetic field lines of a toroidal coil are entirely contained witnin tne coil and = 0 outside. This can be checked by using a flip-coil, Hall probe, or compass needle near the toroidal coil.

However, the lines of vector potential circle the flux lines:

So A is not zero outside the coil.

If a wire is threaded through the hole of the toroid and returned through the hole, case 1, no galvanometer deflection is seen as B is switched on and off. But if the wire is threaded through the hole and returned around the coil, case 2, a galvanometer deflection will be seen from = -d/dt.