Note that the electric field is always perpendicular to the equipotential surface. Hence, the equipotential surfaces are going to be infinite plane sheets parallel to the x-y plane.
Also, the electric field strength is proportional to the distance between the surfaces. Hence, the surfaces will be evenly spaced.
Let charge +q and -q be separated by distance 2a. Let origin be at the centre of the two charges. Consider any arbitrary point P (x,0).
Let ra be the distance of point P from the positive charge and rb be the distance of the point P from the negative charge.
The electric potential at point P is given by:
We have two cases:
Case I: and
Case II: and
Case III: and
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