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1. The problem statement, all variables and given/known data

Consider a magnetic field B = K(x^{3}z^{2},0, -x^{2}z^{3})sinωt in the region of interest, where K and ω are positive constants and t is variable time. Show that the magnitude of the induced emf around a circle R in the plane z = a with its center at x = 0, y = 0, z = a is:

ε = (K/4)∏a^{3}R^{4}ωcosωt

2. Relevant equations

Flux_{b}= ∫B . dA

3. The attempt at a solution

Since the normal vector points in the k direction, we only have to worry about B_{z}.

∫B_{z}dydx. So -∫∫(sinwt)x^{2}a^{3}dydx.

The make the change to polar:

-aK^{3}∫∫(sinwt)(rcosθ)^{2}r dr dθ = -(K/4)a^{3}R^{4}∫cosθsin(wt) dθ.

This doesn't get me anywhere. I'm not really sure what I'm supposed to be integrating over, which is probably why I'm stuck.

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# Homework Help: Show what the magnitude of induced emf

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