26.4 Maxwell-Ampère law

This is a sequel to post 26.03, so I suggest you read that first. Maxwell realised that Ampère’s law applied only when an electric current, in a conductor enclosed by a magnetic field loop, was constant. If the current changes, for any reason, in the first picture of post 26.03, then equation 1 (of post 26.03) must be modified. Maxwell developed this idea by considering a capacitor, consisting of two parallel plates, as described in post 18.19, in a circuit where the current was changing. There is no current flowing between the plates (because the capacitor stores charge), but Maxwell realised that he could extend Ampère’s law by considering a hypothetical current called the displacement current. When the current in a circuit changes, the charge on the capacitor changes (see post 18.19) so that the electrical field, between the plates, changes (see post 16.25). When the electrical field changes, the associated magnetic field must also change; it may help to think of the example of…