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Asked in GSEB Board March 2020 · Equipotential surfaces and V-r graphs
Idea: for a small step d⃗l, the change in potential is dV = -⃗E· d⃗l = -E dl cos θ.
On an equipotential surface dV = 0 for every step taken along the surface.
With ⃗E eq 0 this needs cos θ = 0, i.e. θ = 90°, for every direction lying in the surface.
So the field is perpendicular (normal) to the equipotential surface at every point.
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