A stationary circular conducting loop of resistance R and constant area A lies in the x - y plane. A uniform magnetic field is applied in the z -direction, and its magnitude varies with time t as B = B₀(1 - t) , where B₀ and are positive constants. Which of the following correctly describes the qualitative behaviour of the electrical power P dissipated in the loop as a function of time?

Step-by-step solution

The magnetic flux passing through the loop is = B A = A B₀(1 - t) . According to Faraday's law, the induced emf is: = - d dt = -A B₀ d dt (1 - t) = -A B₀ t The power P dissipated in the loop is: P = ^2 R = (-A B₀ t)^2 R = A^2 B₀^2 ^2 R ^2 t The power P varies as ^2 t . At t = 0 , P = 0 . As time progresses, ^2 t increases to a maximum of 1 and then returns to 0 periodically. Since it is a squared quantity, the power never becomes negative. Therefore, the graph of P versus t is a periodic curve that starts from zero