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# Electron potential of spherical conductor

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Find the electron potential inside and outside of a spherical conductor of radius R = 15 cm carrying a charge Q = 10^-9 C. Evaluate your results for f = 5 cm and r = 20 cm, assuming V = 0 at infinity. Sketch the potential as a function of r. What is the capacitance of the conducting sphere?

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#### Solution Preview

Please see the attached file.

We shall use Gauss law to calculate the potential of a conducting sphere.

Gauss law states that the flux of an electric field through any enclosed surface is proportional to the charge enclosed by the surface.

Now, in most cases the integral can not be solved analytically. However for spherical symmetry we can simplify the integral considerably.

First, due to the isotropic nature of the system we can conclude that the electric field has spherical symmetric as well. Also, this means that the electric field is radial.

Hence, if we choose a spherical Gauss surface, the electric field will be constant and perpendicular to the surface.

Then:

The first integration takes advantage of the fact that the electric ...

#### Solution Summary

This solution explains how to find the electron potential inside and outside of a spherical conductor.

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