Question

Answer the following question:
Explain why, for any charge configuration, the equi potential surface through a point is normal to the electric field at that point.
Draw a sketch of equi potential surfaces due to a single charge (-q). depicting the electric field lines due to the charge.
Obtain an expression for the work done to dissociate the system of three charges placed at the vertices of an equilateral triangle of side 'a' as shown alongside.

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Solution
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The work done in moving a charge from one point to another on an equipotential surface is zero. If the field is not normal to an equipotential surface, it would have a non-zero component along the surface. This would imply that work would have to be done to move a charge on the surface which is contradictory to the definition of euipotential surface.

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