# Equipotential Surfaces | Properties

## Relation Between Electric Field & Electric Potential-

Before you go through this article, make sure that you have gone through the previous article on Relation Between Electric Field & Electric Potential.

We have learnt-

• The relation between electric field and electric potential is given by-

• When we move in the direction of electric field, the electric potential decreases.
• When we move in the opposite direction of electric field, the electric potential increases.
• When we move perpendicular to the direction of electric field, the electric potential remains the same.

## Equipotential Surfaces-

 Any surface (real or imaginary) that has the same value of electric potential at every point on it is called an equipotential surface. OR Locus of all such points at which electric potential is constant is called an equipotential surface.

Now, we shall discuss the properties of equipotential surfaces.

## Properties of Equipotential Surfaces-

### Property-01:

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

#### Explanation-

The work done in moving a test charge q0 in an electric field is given by-

Since on an equipotential surface, every point has the same value of electric potential. So, Vf – Vi = 0.

Thus, work done in moving a test charge on an equipotential surface is zero.

### Property-02:

 Electric field is always normal to the equipotential surface at every point.

#### Explanation-

• If the electric field is not perpendicular to the equipotential surface, then there would exist a component of electric field along the equipotential surface.
• Hence, some work has to be done in moving a test charge on an equipotential surface.
• But work done in moving a test charge on an equipotential surface is zero.

Hence, electric field is always perpendicular to the equipotential surface.

### Property-03:

 Two equipotential surfaces can never intersect each other.

#### Explanation-

If two equipotential surfaces intersect each other, then at the point of intersection, there will be two values of the electric potential which is not possible.

Hence, two equipotential surfaces can never intersect each other.

### Property-04:

 Equipotential surfaces are closer together in the regions of strong electric field and farther apart in the regions of weak electric field.

#### Explanation-

We know, the relation between electric field and electric potential is given by-

• Since dV = constant on an equipotential surface, so dr ∝ 1/E.
• Thus, if E is strong i.e. large, dr will be small i.e. the separation of equipotential surfaces will be smaller and vice-versa.

Thus, equipotential surfaces are closer in the region of strong electric field and far apart in the region of weak electric field.