# Equipotential Surfaces > Equipotential surfaces in JEE Physics: perpendicular to field lines, zero work on the surface, spacing versus field strength and standard shapes for charges. - Canonical URL: https://prepelephant.com/topics/jee/physics/equipotential-surfaces - Exam / course: JEE · Subject: Physics - Publisher: PrepElephant (https://prepelephant.com) — Prepared and reviewed by the PrepElephant Academic Review Team - First published: 2026-10-02 - Last updated: 2026-10-02 - How to cite: "Equipotential Surfaces", PrepElephant, https://prepelephant.com/topics/jee/physics/equipotential-surfaces ## Direct answer Walk along an equipotential surface and the electric field does no work on you: the surface is the locus of constant potential, and since work is q times potential difference, moving any charge on it costs nothing. This single fact forces the geometry — the field must be perpendicular to the surface everywhere (any parallel component would do work along the surface), so equipotentials and field lines always intersect at right angles, field lines plunging from high potential toward low. A point charge wears concentric spheres as equipotentials, a uniform field dresses in parallel planes, and a charged conductor is a single equipotential volume — surface and interior alike. Their spacing is a field strength gauge: where equipotentials crowd, the field is strong (E = −dV/dr is the steepness of potential change), and where they spread, it is weak. ## What you must remember - **Definition:** locus of points at one potential; no work is done moving a charge anywhere on it, W = qΔV = 0. - **Perpendicularity:** E is normal to the equipotential at every point; field lines and equipotentials form mutually perpendicular families, with E pointing from higher to lower potential. - **No intersection:** two equipotentials never cross (a point cannot carry two potentials). - **Standard shapes:** point charge → concentric spheres; uniform field → parallel planes perpendicular to E; charged conductor → the entire conductor (surface plus interior) is one equipotential. - **Spacing as field meter:** closely spaced equipotentials mean a strong field since E = −dV/dr; equal-potential-step drawings directly visualise where force is largest. - **Conductor interior:** E = 0 inside means dV/dr = 0, so the whole body sits at one potential; a cavity inside (with no enclosed charge) is field-free and at that same potential — shielding. - **Dipole pattern:** equipotentials of a dipole are lobed surfaces, tightest near the charges where 1/r² fields dominate, and nearly planar far away at potentials approaching zero. ## Drawing the family for standard cases Build the pictures from the rules rather than memory. A point charge: V = kq/r gives spherical equipotentials — going from 100 V to 50 V doubles the radius, so successive spheres spread as 1/r while radial field lines cross each at 90°, both families declaring the inverse-square weakening. Between parallel plates 100 V apart: equally spaced 1 V planes mean E = 100 V/m from high to low; wherever the spacing narrows the field is stronger — field strength read off an equipotential map at a glance. The conductor case closes the set. Put a charge on an irregular conductor: the whole body is one potential, but the surrounding shells crowd tightly near sharp points (strong local field) and spread wide over flat regions — the lightning rod's tip squeezes the neighbouring surfaces so close that the field exceeds air's breakdown and charge escapes before a strike accumulates. One algebra nugget: for V(x) = 5x² volts, E = −dV/dx = −10x V/m, so at x = 0.2 m the field is 2 V/m pointing toward decreasing x — a potential function turned into field direction and magnitude, the analytic twin of the spacing rule. ## Equipotential questions in JEE The zero-work fact generates the classic pair: work is zero on an equipotential but nonzero between two different equipotentials (W = qΔV regardless of path — another conservative-field hallmark worth stating), and the options confuse the two statements deliberately. Second, perpendicularity appears in reverse: "the equipotentials of a uniform field are planes perpendicular to the field" and their spacing is uniform; any diagram showing tilted or curved surfaces in a uniform field is wrong on sight. Third, the conductor statement set: interior field zero, interior potential constant and equal to the surface value (not zero!), cavity field-free — the "constant, not zero" distinction is a reliable discriminator in assertion-reason format. Fourth, spacing reading: given a diagram with labelled potentials, compare field strengths in two regions by steps per distance — closer means stronger, no computation invited. Fifth, E = −dV/dr direction: the negative sign means the field points down the potential hill, and students who drop the sign get the direction reversed. Main tests these as single-concept items; Advanced combines a conductor with an external field, or asks how the family must continue given symmetry and perpendicularity. ## Frequently asked questions ### Why is no work done in moving a charge on an equipotential surface? Because work equals charge times potential difference, and the potential difference between any two points of the same surface is zero by definition. ### What is the relationship between field lines and equipotential surfaces? They are everywhere mutually perpendicular, with field lines directed from surfaces of higher potential toward lower potential. ### What shapes do equipotentials take for a point charge and a uniform field? Concentric spheres around a point charge, and parallel planes perpendicular to the field direction in a uniform field. ### Why is the entire volume of a charged conductor an equipotential? In electrostatic equilibrium the interior field is zero, so dV/dr = 0 throughout the material — the potential is constant from core to surface, though not necessarily zero. ### What does close spacing of equipotential surfaces indicate? A strong electric field, since E = −dV/dr: the same potential step compressed into less distance means a steeper potential gradient and a larger force on any charge there.