Use Gauss' Law to find the electric field, everywhere,of charge of uniform density [itex]\rho[/itex] occupying the region [itex]a<r<b[/itex], where r is the distance from the origin. Having done this, find the potential.(adsbygoogle = window.adsbygoogle || []).push({});

Ok, so far I said that by Gauss' Law,

[itex]\Phi=\oint_S \vec{E} \cdot \vec{dS} = \int_V \nabla \cdot \vec{E} dV = \frac{Q}{\epsilon_0} = \frac{1}{\epsilon_0} \int_V \rho dV [/itex]

and since V is arbitrary I obtain Poisson's Equation

[itex]\nabla \cdot \vec{E} = \frac{\rho}{\epsilon_0} [/itex]

I just can't see how to rearrange for E???

Initially I was considering integrating something over a sphere of radius b and then over a sphere of radius a and subtracting them but I don't have any idea what to integrate.

Are either of these ideas useful? If so, what do I do next? If not, can you suggest something?

Cheers

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# Homework Help: Use Gauss' Law to find the electric field

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