Equipotential Surfaces

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Sketching the surfaces of constant potential around a single isolated positive point charge on a whiteboard, a teacher asks about their shape, so what are they?

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An equipotential surface is one on which the electric potential has the same value everywhere, so no work is done moving a charge along it, a concept detailed in NCERT Class 12, Chapter 2 (Electrostatic Potential and Capacitance). For a point charge the potential $V = \frac{kq}{r}$ depends only on the radial distance $r$, so all points at equal $r$ share the same potential, forming concentric spheres. These surfaces are always perpendicular to the field lines, because any tangential field component would do work and violate the constant-potential condition. The option of parallel planes is wrong because that describes the equipotentials of a uniform field, not a point charge. The option of radial lines is wrong because those are the field lines themselves, which point along the potential gradient, not along constant potential. The option of coaxial cylinders is wrong because that geometry belongs to a line charge. A consistency check confirms the spherical symmetry: since a point charge looks identical from all directions, its equipotentials must inherit that symmetry, and perpendicularity to radial field lines is automatically satisfied by spheres.

Equipotential Surfaces

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