Why does excess positive charge stay on the surface of a conductor?
This is what I understood from:
How does positive charge spread out in conductors?
and other resources on the web:
- If there is a electric field inside the conductor they will pull on the electrons
- Therefore there can be no field inside the conductor
- It follows from Gauss's Law that there are no charges inside
My questions:
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If there are positive charges inside the conductor, they will attract the electrons. But the electrons are already being attracted by the nucleus they belong to so why would they move? All electrons have electric fields already acting on them (the electric field of the nucleus) so why would adding new ones make a difference?
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If the positive charges are distributed on the surface, the field would only be zero right at the centre.The fields would cancel out in the centre because of symmetry but the field anywhere other than the centre would be non-zero. So how would the electrons be an equilibrium?
Please see the details on the bounty
Best Answer
The defining property of a conductor is that charge is free to move within it. Hence, if there existed an electric field within the conducting medium, charge would move until the field became zero. It follows that $\vec{E} = 0$ inside of a conductor.
Gauss's law therefore implies: $$ \rho=\epsilon_0\nabla\cdot\vec{E}=0, $$
since $\vec{E} = 0$ within the bulk of the conductor, all of the excess charge must reside on the surface.
To address your two questions specifically;