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

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.



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