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**JEE Mains**

## Equipotential surfaces

Surfaces having same potential are termed as equipotential surfaces

The properties of equipotential surfaces can be summarized as follows:

The properties of equipotential surfaces can be summarized as follows:

- The electric field lines are normal to the equipotentials and are directed from higher to lower potentials.
- By symmetry, the equipotential surfaces produced by a point charge form a family of concentric spheres, and for a constant electric field, a family of planes normal to the field lines.
- The tangential component of the electric field along the equipotential surface is zero, otherwise non-vanishing work would be done to move a charge from one point on the surface to the other.
- Work done in moving a particle along an equipotential surface is zero.

Within a spherical charge distribution of charge density $ρ(r)$, N equipotential surfaces of potential $V_{0},V_{0}+ΔV,V_{0}+2ΔV,.....,V_{0}+NΔV(ΔV>0)$, are drawn and have increasing radii $r_{0},r_{1},r_{2},.....r_{N}$, respectively. If the difference in the radii of the surfaces is constant for all values of $V_{0}$ and $ΔV$ then :