How Is EMF Induced in a Loop Within a Solenoid?

[kinof]

Homework Statement

A small loop with area 6.8 mm^2 is placed in a long solenoid with 854 turns/cm and a sinusoidally varying current w/ amplitude 1.28 A and angular frequency of 212 rad/s. What is the amplitude of the emf induced in the loop?

Homework Equations

$\textbf{B}=\mu_0 in$
$\Phi_B = BA$
$emf = \frac{d\Phi_B}{dt}$

The Attempt at a Solution

Since the current is changing, the emf through the loop should be $\mu_0 n A \frac{di}{dt}$
If the angular frequency is 212 rad/s, then the current changes by 1.28 A in half a period, which is $\frac{\pi}{212}$ seconds. So the induced emf should be 6.29E-5 V, but the answer is .198 mV.

 

[rude man]

1.

If the angular frequency is 212 rad/s, then the current changes by 1.28 A in half a period, which is $\frac{\pi}{212}$ seconds. So the induced emf should be 6.29E-5 V, but the answer is .198 mV.

Does not make sense to me.

If the current is i*sin(wt), what is di/dt? The rest of what you did looks OK.

BTW I also get 0.198 mV.