# Use Gauss's Law to find the electic field, electric potential

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A solid insulating sphere has a radius A and net charge of +Q. The insulating sphere has a uniform charge density. a conducting sphere of inner radius B and outer radius C surrounds it.

I.

Use Gauss's Law to find the Electic Field for R<A

II.

Use Gauss's Law to find the Electic Field for A<R<B

III.

Use Gauss's Law to find the Electic Field for B<R<C

IV.

Use Gauss's Law to find the Electic Field for R>C

V.

What is the electric potential for R < A

VI.

What is the electric potential for R = A

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1) For R<A

Choose a sphere of radius R<A as your Gaussian surface. Let p be the charge density of the insulator, and let V' be the volume of your Gaussian sphere. Then the charge enclosed by the Gaussian surface is:

Q_in = pV'

where V' = (4/3)*pi*R^3

Since the magnitude of the electric field is constant everywhere on the spherical Gaussian surface and is normal to the surface at each point, gauss' law gives:

Electric flux through surface = E*SurfaceArea

= E*4*pi*R^2

= ...

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