A rectangular wire loop with 25 turns, length L = 20.0 cm and width W = 10.0 cm

Question

A rectangular wire loop with 25 turns, length L = 20.0 cm and width W = 10.0 cm is rotating with a constant angular velocity omega = 2.00 rad/s. At time t = 0 s the plane of the loop is perpendicular to a magnetic field given by B = Ct^2, where C = 4.00 T/s^2.

(a) What is the induced emf when t = 2.50 s?

(b) If the wire loop has a total resistance of 25.0 ohms, what is the induced current in the wire at this time? What is the direction of this current when viewed from the tip of the area vector toward the loop?

Hint: The flux through the loop is BAcos(phi)where phi= (omega)t. (Explain why it has this form!)

Explanation / Answer

flux=B.A=B*A*cos(theta) theta=w*t emf=d(flux)/dt=A*4*2*t*cos(w*t)-4*A*t^2*w*sin(w*t) at t=2.5 s emf=0.114+0.958=1.072 V i=emf/R=0.0428 A direction is clockwise

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