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Equipotential surfaces are surfaces where electric potential has the same value everywhere. They provide a complementary picture to electric field lines, with four fundamental properties: (1) E is always perpendicular to equipotential surfaces — any tangential E component would cause charge motion along the surface, contradicting constant V; (2) No work is done moving a charge along an equipotential surface since W = q*delta(V) = 0; (3) They never intersect (V is single-valued); (4) Closer spacing indicates stronger E.

For a point charge: concentric spheres. For a uniform field: parallel planes perpendicular to E. For a dipole: complex surfaces with the equatorial plane at V = 0. For multiple charges: distorted but non-intersecting surfaces. Every conductor surface in equilibrium is equipotential.

The mathematical relationship E = -grad(V) = -(dV/dx, dV/dy, dV/dz) means the field can be obtained from the potential by differentiation. This is often the easiest method for complex charge distributions: calculate V (scalar sum), then differentiate to get E.

In JEE problems, you may be given V as a function of coordinates and asked to find E, or asked to sketch equipotential surfaces for a given charge configuration. Common problem: if V = $ax^2$ + by + c, then $E_x$ = -2ax, $E_y$ = -b, $E_z$ = 0. The field strength and direction vary with position.