3. Problem: Induction Problem 2 a) Consider a square loop of wire with side of l

Question

3. Problem: Induction Problem 2
a) Consider a square loop of wire with side of length l that has internalresistance R. The loop is initially oriented so that its vector area is parallel

to a uniform magnetic eld

B = B0ˆ

k. The loop is then rotated about anaxis through the centerline at a constant angular frequency , such that themagnetic ux through the loop changes as it rotates. Obtain an expressionfor the current in the loop as a function of time.b) What if it is rotated about an axis through a diagonal instead?

Explanation / Answer

a) magntic flux through the loop = A*B*cos(theta)

= l^2*B*cos(w*t)

induced emf = the rate of change of magnetic flux through the loop

= -d(l^2*B*cos(w*t))/dt

= -l^2*B*(-sin(w*t))*w

= B*l^2*w*sin(w*t)

b) same.

induced emf = B*l^2*w*sin(w*t)

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