Question

An infinite nonconducting sheet has a surface charge density on one side. How far apart are equipotential surfaces whose potentials differ by ?

Medium

Solution

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The electric field produced by an infinite sheet of charge has magnitude where   is the surface charge density. The field is normal to the sheet and is uniform. Place the origin of a coordinate system at the sheet and take the x axis to be parallel to the field and positive in the direction of the field. Then the electric potential is

                 

where is the potential at the sheet. The equipotential surfaces are surfaces of constant that is, they are planes that are parallel to the plane of charge. If two surfaces are separated by then their potentials differ in magnitude by
                     
Thus,
                     

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