# Loop inside a solenoid, finding induced current

by Sekonda
Tags: current, induced, inside, loop, solenoid
 P: 209 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