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 Potential on the Surface of a Charged Conductor
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.  
   
Conclusions:  
N.B. These conclusions apply when considering static conditions in a perfect conductor.  
1. All points on the surface of a charged conductor are at the same potential.  
2. There can be no electric field in a conductor.  
   
Experiments also show that there is no field inside a hollow charged 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  
   
assuming the sphere is in a vacuum.  
Inside the sphere, there is no electric field so all points are at the same potential as the surface.  
Therefore  
   
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