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Asked in GSEB Board July 2021 · Equipotential surfaces and V-r graphs
Idea: V is the same everywhere on an equipotential surface, so no work is done in moving a charge along it.
For a step Δ s along the surface, W = qE Δ s cos θ, where θ is the angle between ⃗E and the step.
This vanishes for every direction lying in the surface only if ⃗E has no component along the surface, i.e. θ = 90°.
So the equipotential surface through any point is normal to the electric field there.
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