- #1

auk411

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**Someone who knows what they are talking about: Show what the magnitude of induced emf**

## Homework Statement

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

## Homework Equations

Flux

_{b}= ∫B . dA

## 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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