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kaustavdgreat
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1.Prove that free charge resides on the surface of a conductor.(Using Gauss's law or laws of capacitance)
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
Homework Equations
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