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Bhumble

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## Homework Statement

Picture the electron as a uniformly charged spherical shell, with charge e and radius R, spinning at angular velocity [tex]\omega[/tex].

(a) Calculate the total energy contained in the electromagnetic fields.

## Homework Equations

[tex]\oint \vec{B} \bullet d\vec{l} = \mu_0 I_{enc} + \mu_0 \epsilon_0 \int \frac{d\vec{E}}{dt} \bullet d\vec{a}[/tex]

[tex]U_{em} = \frac{1}{2} \int \epsilon_0 E^{2} + \frac{1}{\mu_0} B^{2} d\tau [/tex]

## The Attempt at a Solution

So the solution should just be a matter of plugging in to the second equation. My dilemma is actually in finding the fields.

E(r<R) = 0 by symmetry,

[tex]E(r>R) = \frac{1}{4 \pi \epsilon_0} \frac{e}{r^{2}} \hat{r} [/tex]

Per the maxwell amperian loop I get B(r<R) = 0 but this is apparently incorrect and I don't understand why.

And B(r>R) = dE/dt (4pi r^2)/(2pi r).

My problems seem to be with determining the magnetic field. Does anyone see what I'm missing here?