A circular conducting loop of radius r and total resistance R is fixed in space. A spatially uniform magnetic field perpendicular to the plane of the loop increases in magnitude according to B(t)=B0+kt, where B0 and k are positive constants. The field is directed into the page.
Assume the field begins changing at time t=0 and the loop’s dimensions remain constant.
(a) Calculate the magnitude of the induced emf in the loop at an arbitrary time t.
(b) Determine the magnitude and direction of the induced current I(t) at that time.
(c) Find the instantaneous electrical power P(t) that is dissipated in the loop’s resistance.
(d) Derive an expression for the total electrical energy E(T) converted to thermal energy in the loop during the time interval from t=0 to t=T.