(adsbygoogle = window.adsbygoogle || []).push({}); 1.Prove that free charge resides on the surface of a conductor.(Using Gauss's law or laws of capacitance)

2. Relevant equations

3. The attempt at a solution

I could not figure out how to prove this using Gauss's law,though i tried to solve it using the laws of capacitance.This is what i did-

Let us consider a spherical conductor of radius R having charge Q.

The potential of the conductor (V)=Q/C

If the charges are spread in such a way that it forms a spherical shell of radius r then, C=r

where [tex]r\leq{R}[/tex]

Now the maximum value of r should be R

We know that every system tends to attain a state of minimum potential.

V will be min, when C is max or, C=R

So, r=R

Hence, the charge will always reside on the surface.

Thnx in advance

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# Homework Help: Why does free charge reside on the surface of a conductor?

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