Question

What is an equipotential surface?

Answer 1

Electric potential is the potential energy per unit charge. Potential on an equipotential surface is constant through the surface. The direction of the electric field is perpendicular to the equipotential surface.

Complete step-by-step answer :
Electric potential at the point is equal to the potential energy of a unit charge placed at that point.
Equipotential surface is a surface where all the points lying on the surface have the same electric potential. This means that a charge will have the same potential energy at every point on the equipotential surface.
We know that the change in potential energy is equal to the negative of work done by the electric field on the charge. However, if the charge is moved on an equipotential surface, the change in the potential energy is zero. Therefore, the work done on the charge is zero.
We also know that when the work done is zero, the directions of the force and the displacement of the particle are perpendicular to each other. And the direction of the electric field is parallel to the direction of the electric force. Therefore, the electric field and the displacement of the charge are perpendicular. Since the displacement on the equipotential surface, this means that the direction of the electric field is always perpendicular to the equipotential surface.
The equipotential surface for a point charge q is a sphere with the charge at its centre.
The equipotential surface for an infinite line of charge is a cylinder with the line of charge at its centre.

Note :This concept of equipotential surface can be applied to the gravitation as well.
To find an equipotential surface of a system trace the points where the electric field is perpendicular to the curve formed joining the points.