# 1 charge at the center and many uniformly distributed on the surface of a perfect ideal conducting solid sphere

Suppose there is a perfect ideal conducting solid sphere. Suppose somehow a charge of $+Q$ is kept exactly at the center of the sphere and its surface is also given a $+Q$ charge uniformly distributed at the same time.

We know electric field inside a charged conductor is zero. But in this situation, a $+Q$ charge has appeared exactly at the center of the charged conductor. Will the electric field still be zero? If there is electric field inside,since net force on the center charge is zero and since the surface charges cannot go outside the sphere, the situation is like holding the surface charges with rigid sticks from the center, can a situation like this be created or will the center charge also go to the surface??

Lets take an electron and put it at the center and many electrons uniformly distributed on the surface of the sphere at the same time. Now net force on the electron is zero. Will it stay there and if we move it slightly it will come to the surface or will it come to surface anyway?

## 2 Answers

If the sphere is conducting, then the field at any point within the conductor is zero: the field within any ideal conductor is everywhere zero. So if you displace the center charge, it will just stay where you put it. It will not move to the surface.

Consider the same situation but with vacuum inside the sphere instead of an ideal conductor. The field inside a uniformly charged sphere is zero, so the same result obtains: if you displace the charge slightly, it will just stay where you put it. It will not move to the surface.

• Lets take an electron and put it at the center and many electrons uniformly distributed on the surface of the neutral sphere at the same time. Now net force on the electron is zero. Will it stay there and if we moe it slightly it will come to surface or will it come to surface anyway? – Jolie Feb 23 '14 at 20:45
• It will stay put. – garyp Feb 23 '14 at 22:00

From the Guass law it follows that for a solid spherical shell, charge on the surface also behaves as if concentrated at its center. So, instead of spreading $+Q$ charge on the surface and placing $+Q$ charge at the center, you can directly spread $+2Q$ charge on the surface for the same effect. So, considering this, yes it is possible to create such a situation. I hope this helped.

• Lets take an electron and put it at the center and many electrons uniformly distributed on the surface of the neutral solid sphere at the same time. Now net force on the electron is zero. Will it stay there and if we moe it slightly it will come to surface or will it come to surface anyway? – Jolie Feb 23 '14 at 20:45
• As the nature of charge on the surface and at the center is same, due to symmetry forces on the electron at center gets cancelled and thus there will be no force acting on it. So, it will stay there. When you move it slightly from the center, there will be imbalance due to difference in distance of the electron to the radially opposite surface points, thus net force don't stay zero. Here, electron will come to the surface towards which it was moved. – Immortal Player Feb 23 '14 at 21:58