or

Why Equipotential surfaces are always at right angles to lines of electric force?

For an equipotential surface,

Change in potential difference, ∆V = 0

Work done = q×∆V = q×0 = 0

Also,

Work done = Fs cosA = 0

Where, F = Force due to charges,

s = distance between charged bodies, and

A = angled between direction of F and s

Since, the equipotential surface is formed due to cancellation of equal and opposite electric fields, F and s cannot be 0.

So, Work done = 0 if and only if cos A = 0 → A = 90°

Hence, the equipotential surfaces are always at right angles to lines of electric force.