A circular loop of flexible iron wire has an initial circumference of 165.0 cm, but its circumference is decreasing at a constant rate of 12.0 cm/s due to a tangential pull on the wire. The loop is in a constant uniform magnetic field of magnitude 0.500 T, which is oriented perpendicular to the plane of the loop.
Find the induced EMF in the loop at the instant when 9 seconds have passed.
I thought that I could answer this like I delineate here:
1. the induced EMF = - d(phi_B)/dt (magnetic flux)
and magnetic flux = line integral of B*dA = B*A*sin(90) = B*A
If the circumference is decreasing at a rate of 12 cm/s then because C=2*pi*r
r = C/2*pi = 1.9098
so at t=9, r = 17.188
magnetic flux = B*A = (0.500)*(pi*17.88)^2 = 1458
This is not the correct answer. What am I doing wrong?
The circumference and hence the area of a circular loop is varying. The induced EMF is calculated.