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Loop inside a solenoid, finding induced current 
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#1
May1212, 11:26 AM

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: [tex]\varepsilon =\oint _{C}\vec{E}\cdot d\vec{L}[/tex] and by stokes theorem I equated this to: [tex]\oint _{C}\vec{E}\cdot d\vec{L}=\int\int_{S,open}\left (\bigtriangledown \times \vec{E} \right )\cdot d\vec{A}[/tex] 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: [tex]I(t)=\frac{\omega \pi r^2B_{0}cos(\omega t)}{9R}[/tex] Is this all right or have I made a mistake, and if so where? Thank you very much for your time, SK 


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