# Homework Help: Loop inside a solenoid, finding induced current

1. May 12, 2012

### Sekonda

Hey,

The question concerns a basic solenoid with an oscillating current, we have a loop inside with a particular resistance and we want to determine the current induced in this particular loop. The question is in the image below:

Right, well it tells us to determine the electromotive force; so I used the:

$$\varepsilon =\oint _{C}\vec{E}\cdot d\vec{L}$$

and by stokes theorem I equated this to:

$$\oint _{C}\vec{E}\cdot d\vec{L}=\int\int_{S,open}\left (\bigtriangledown \times \vec{E} \right )\cdot d\vec{A}$$

and by using Faraday's Law to find the cross product of E via the derivative of the magnetic field with respects to time, I put this into the above RHS equation to determine the electromotive force.

I attained the final current as:

$$I(t)=-\frac{\omega \pi r^2B_{0}cos(\omega t)}{9R}$$

Is this all right or have I made a mistake, and if so where?

Thank you very much for your time,
SK