(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

A long solenoid of radius a , is driven by an alternating current , so that the field inside is sinusoidal: B(t)=B_{0}cos(omega*t)z-hat. A circular loop of wire, of raduis a/2 and resistance R, is placed inside the solenoid and coaxial with it. Find the current induced in the loop , as a function of time.

2. Relevant equations

I=[tex]\epsilon[/tex]/R

[tex]\Phi[/tex]=[tex]\int[/tex]B[tex]\cdot[/tex] da

[tex]\epsilon[/tex]=[tex]\int[/tex]E[tex]\cdot[/tex]dl=[tex]\int[/tex](dB/dt)[tex]\cdot[/tex]da

3. The attempt at a solution

dB/dt=-omega*B_{0}sin(omega*t)z-hat

[tex]\epsilon[/tex]=[tex]\int[/tex]omega*B_{0}sin(omega*t) da, since the area of a circle is pi*r^{2}, da is just pi*r^{2}

I=omega*B_{0}*sin(omega*t)*[tex]\pi[/tex]a^{2}/(R)

episilon is supposed to be the electromotive force BTW.

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# Homework Help: Faraday Law problem

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