A conducting loop of finite resistance lies on the x - y plane. There is a constant magnetic field in the z direction. The area of the loop varies with time t , as A=A₀(1+ t) in appropriate units. The figure that correctly indicates the qualitative behaviour of the power P dissipated in the loop as a function of time is :

Step-by-step solution

The magnetic flux passing through the loop is given by: = B A Given that the area varies with time as A = A₀(1 + t) and the magnetic field B is constant, the flux is: = B A₀(1 + t) According to Faraday's law of electromagnetic induction, the induced emf is: = - d dt = -B A₀ d dt (1 + t) = -B A₀ t The power P dissipated in the loop of resistance R is: P = ^2 R = (-B A₀ t)^2 R = B^2 A₀^2 R ^2 t From this expression, we can see that the power P varies as ^2 t . At t = 0 , P = B^2 A₀^2 R ^2(0) = B^2 A₀^2 R (which is a