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Electric Images

Let XY be an infinite conducting plane which is earthed. The plane is at zero potential. Let a point chare +q be placed at the point A at a distance d from the plane. Due to electrostatic induction, a negative charge is induced on the plane XY. The combined effect of the positive charge at A and the negative charge induced at any point of the conducting plane should make the potential of that point equal to zero.

Now, remove the plane XY. Place a charge – q at B such that AO = BO = d.

     Potential at any point}    = __+q___ - ____q____ = 0
                      ______________4π ε0       4π ε0 (BP)

Thus the effect at all points due to the charge +q at A and – q at B is the same as that due to the charge +q at A and –q at B is the same as that due to the charge +q at A and the plane XY. So we can calculate the potential at any point in the region S to the right of XY by replacing the actual system a with its equivalent system b. The charge – q at B is called the electrical image of the charge + q at A.

Definition. An electrical image may be defined as a point-charge on one side of a surface, which will produce on the other side of the surface, the same electric field as is produced by the actual electrification of the surface. The actual electrification of the surface is ignored and the image is used instead to find the field.

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