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=A_0(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 :
C.
The magnetic flux passing through the loop is given by: = B A Given that the area varies with time as A = A_0(1 + t) and the magnetic field B is constant, the flux is: = B A_0(1 + t) According to Faraday's law of electromagnetic induction, the induced emf is: = - d dt = -B A_0 d dt (1 + t) = -B A_0 t The power P dissipated in the loop of resistance R is: P = ^2 R = (-B A_0 t)^2 R = B^2 A_0^2 R ^2 t From this expression, we can see that the power P varies as ^2 t. At t = 0, P = B^2 A_0^2 R ^2(0) = B^2 A_0^2 R (which is a maximum value). At t = 2 , P = 0. The graph of P versus t will start from a maximum positive value, decrease to zero, and then increase again, oscillating between 0 and a maximum value. This behavior is correctly represented by the graph in option (3). Answer:
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