A perfectly conducting filament is formed into a circular ring of radius a. At one point, a resistance R is inserted into the circuit, and at another a battery of voltage V₀ is inserted. Assume that the loop current itself produces negligible magnetic field.

(a) Apply Faraday’s law, Eq. (4), evaluating each side of the equation carefully and independently to show the equality;

(b) Repeat part a, assuming the battery is removed, the ring is closed again, and a linearly increasing B field is applied in a direction normal to the loop surface.