The picture below shows an edge-on view of an infinite sheet of positive charge

Question

The picture below shows an edge-on view of an infinite sheet of positive charge density sigma. (a) How much work is done by the electric field of the sheet as a small test charge q_0 is moved from an initial position on the sheet to a final position located a perpendicular distance z away from the sheet? (b) Use the answer from part (a) to show that the electric potential of an infinite sheet of charge can be expressed by the equation V = V_0 - (sigma/2 epsilon_0)Z where V_0 is the potential at the surface of the sheet.

Explanation / Answer

A) here electric field is constant = sigma/2eo

Work done = Fz = q* (sigma /2eo) *z

B) Potential change =W/q = (sigma /2eo) *z

V = Vo - (sigma /2eo) *z

Hence shown

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