A locus of points in space that all have the same potential is called an equipotential surface.

`text(Properties of equipotential surfaces :)`

(i) Work done in moving a charge over an equaipotential surface is zero. Thus the work done in moving a charge +q from one point A to another point Bon a equipotential surface is given by, Fig1

`W_(AB) = -q(V_B - V_A) = -q(0) = 0`

(ii) The electric field is always perpendicular to an equipotential surface. Referring to figure, we have Fig 2

`dV = -vecE.vec(dl)`

Since `dV = 0` for an equipotential surface,

`vecE.vec(dl) = 0` means that `vecE bot vec(dl)`

(iii)The spacing between equipotential surfaces enables us to identity regions of strong and weak field.
We know that `E = - (dV)/(dr)`

For a given dV (i.e., constant dV), `E prop 1/(dr),` This means that where the equipotential surfaces are crowded, the electric field intensity is greater and vice-versa. In the above figure equipotential surfaces having constant potrntial difference between two consecutive surfaces are shown.

(iv) Two equipotential surfaces can be never intersect. If two equipotential surfaces could intersect, then at the point of intersection there would be two values of electric potential which is not possible.