A single circular loop of resistance 10Ω, area A, and N turns is kept perpendicular to a uniform magnetic field whose magnitude varies with time according to B(t)=B0e−kt, where B0 and k are positive constants.
(i) Derive an expression for the instantaneous emf induced in the loop in terms of N, A, B0, k, and t.
(ii) Hence obtain an expression for the instantaneous current in the loop.
(iii) Calculate the total thermal energy produced in the loop from t=0 to t=∞.