Experiments show that the charge on a conductor stays on the surface.

Consider a situation in which two points on the surface of a conductor are at different potentials. In this situation free electrons at one point have more potential energy than at the other point and so they will move. The movement of charge will stop when all points on the surface are at the same potential.

Conclusion

The following conclusions apply when considering static conditions in a perfect conductor.

Potential due to a Charged Hollow Metal Sphere

Outside the sphere the charge can be considered to be a point charge placed at the centre.

Therefore

Inside the sphere, there is no electric field so all points are at the same potential as the surface.

Therefore

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