# Why charges inside a solid metallic sphere tend to go to the surface?

The Question

Why charges inside a solid metallic sphere tend to go to the surface?

The Problem

(Speaking ideally and in the context of classical e-m realm, so don't imagine of atoms, etc.)
Since the dilectric constant of metal is infinite, the two charges won't apply any force on each other. If it is true then what drives the charges on the surface. Or ideally they(charges) really can't appear on the surface?

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Defennder
Homework Helper
You can use Gauss law to see why. The E-field within a conductor is 0. An imaginary closed surface within the sphere would have 0C of charge enclosed in order for the flux through that closed surface to be zero. That implies, by virtue of symmetry and taking the imaginary closed surface to be a sphere, that all net charge must then reside on the surface.

Alternatively, you can view it as the net charges in the solid conducting sphere repelling each other. The "furthest" the charges can travel by means of maximum repulsion would be the surface of the sphere.

Imagine - you put charge on a metal conducting sphere by running a current for a time, (adding or removing electrons). OK - you have extra electrons stuck on it. It will have a voltage relative to other places, and so there will be an electric field between it and other places. But what of the inside of the sphere? Does that space count as "other places"?
Sure it does, but it comes with a condition that is going to kill any voltage gradient that might have existed, because it is a conductor that will run a current to equally redistribute the electrons around its surface.

Imagine also, the sphere hollowed out. There will be no charges on the inside surface of the sphere. High voltage researchers can sit inside a nearly complete metal sphere, with all their equipment, and the outside can be charged to hundreds of thousands of volts.

You can use Gauss law to see why. The E-field within a conductor is 0. An imaginary closed surface within the sphere would have 0C of charge enclosed in order for the flux through that closed surface to be zero. That implies, by virtue of symmetry and taking the imaginary closed surface to be a sphere, that all net charge must then reside on the surface.

Alternatively, you can view it as the net charges in the solid conducting sphere repelling each other. The "furthest" the charges can travel by means of maximum repulsion would be the surface of the sphere.
Well, that's the prob, if the net field inside the conductor is always zero, then why will charges repel? Suppose an already existing sphere, I keep two charges somewhere around the center and they will instantly tend to the surface, if there is not gonna be any e-field, then what will be the driving force for it to take to the surface. Further by Coulomb's Law, since the K=(infinite), the F(net) on either charge is zero, then why the charge will appear on the surface, if no force is acting on it?

Defennder
Homework Helper
The problem is that the scenario you describe is not under electrostatic equilibrium. The electric field in a conductor is zero under electrostatic equilibrium. This is true under steady-state conditions.