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Asked in GSEB Board July 2023 · Equipotential surfaces and V-r graphs
On an equipotential surface V is the same everywhere, so moving a test charge along it takes no work: W=q Δ V=0.
The work for a small step d⃗l is q⃗E·d⃗l.
For this to vanish for every step along the surface, ⃗E must be perpendicular to every such step.
So the field is normal to the equipotential surface at every point, pointing towards lower potential.
Examples: concentric spheres around a point charge, and planes perpendicular to a uniform field.
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