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Loop inside a solenoid, finding induced current

by Sekonda
Tags: current, induced, inside, loop, solenoid
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May12-12, 11:26 AM
P: 209

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,
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