# Induced Electric Field

1. Jul 23, 2006

### DarkWarrior

Hello, I'm stuck (again) on a physics problem.

The problem:

Early in 1981 the Francis Bitter National Magnet Laboratory at M.I.T. commenced operation of a 3.3 cm diameter cylindrical magnet, which produces a 30 T field, then the world's largest steady-state field. The field magnitude can be varied sinusoidally between the limits of 29.6 and 30.9 T at a frequency of 15 Hz. When this is done, what is the maximum value of the magnitude of the induced electric field at a radial distance of 1.6 cm from the axis?

What I've done so far: I've used Faraday's law, and after messing around with the equation I got E = (r/2)(dB/dt). As I understand it, the induced electric field is inside the magnetic field (r is less than R), so I thought this equation was correct.

R= .0165 m
r = .016 m
dB/dt = 19.5 Tesla/second. Since the frequency is 15, you multiply the difference of 30.9 and 29.6 by 15, getting 19.5

However when I plug the numbers in, my answer comes out wrong. Can someone point out where I screwed up? Thank you!

2. Jul 23, 2006

### Andrew Mason

Set up the equation for the field as a function of time (B = sinusoidal term + constant). Then differentiate with respect to time. There will be a factor $\omega = 2\pi/T$ in the equation.

AM