Equipotential surface: Any surface that has same electric potential at every point on the surface of the conductor known as equipotential surface.

Properties of equipotential surface:

1. No work is done in moving test charge over an equipotential surface:

If the test charge q₀ is moved from A to B, the work done will be

W_AB = charge * potential difference

= q₀ (V_B - V_A) 

As the surface is equipotential, so V_B – V_A = 0

Hence work done is zero.

2. Electric field is always normal to the equipotential surface at every point: If the field is not normal to the equipotential surface, it would have non zero component along the surface. So to move a test charge against this component, work has to be done but no work is required to move a test charge along the surface. So the electric field must be normal to the equipotential surface.
3. Equipotential surfaces are closer together in the regions of strong field and farther apart in the regions of weak field:
4. , thus the spacing between the equipotential surface will smaller in the region, where electric field is stronger and vice-versa.
5. No two equipotential surfaces can intersect each other: If they intersect, then there will be two values of electric potential at the point of intersection, which is impossible.

Equipotential surfaces of a various charge systems.

1. Equipotential surface of positive point charge: The equipotential surface of a single point charge are concentric spherical shells with their centres at point charge. The lines of force are radially outwards, so they are perpendicular to the equipotential surface.
2. Equipotential surfaces of two equal and opposite point charges: Electric dipole: These are close together in the region in between the two charges.
3. Equipotential surfaces of two equal positive charges:The equipotential surfaces are far apart in the regions in between the two charges, indicating aweak field in such regions.
4. Equipotential surfaces for a uniform electric field: The lines of force are parallel straight lines and equipotential surface are equidistant parallel planes perpendicular to the lines of force.