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Asked in GSEB Board July 2018 · Equipotential surfaces and V-r graphs
Idea: on an equipotential surface V is the same everywhere, so moving a charge along it takes no work.
Work for a small step Δ s along the surface: W = qE Δ s cos θ, where θ is the angle between ⃗E and the step.
W = 0 for every step along the surface only if cos θ = 0, i.e. θ = 90°.
So field lines always cross equipotential surfaces at right angles: the angle is π/2.
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