A conducting wire loop lies in the plane of the screen, in a region where there's a uniform magnetic field directed into the screen. The loop has radius a and resistance R. Starting at t = 0, the field changes as a function of time, B(t) = B0 e-ct where c and B0 are constants. (a) Write an expression for the magnetic flux through the loop as a function of time. (b) What is the magnitude of the emf induced in the loop? (c) Calculate the power output of the loop as a function of time.
A
(a) Write an expression for the magnetic flux through the loop as a function of time.
(b) What is the magnitude of the emf induced in the loop?
(c) Calculate the power output of the loop as a function of time.
(d) Use your answer from part (c) to obtain the total energy dissipated in the resistance of the loop as the field goes from B = B0 at t = 0 to B = 0 at large times. If you couldn't get (c), you can receive partial credit by describing a solution to this part assuming some function P(t) for the power as a function of time.
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