Equipotential Surfaces: Definition, Properties, Application, Problems and Physics Notes

A surface with a constant potential value at all points on the surface is referred to as an equipotential surface. Also, the potential difference between any two points on the surface is zero. So, no work is done in moving a charge on this surface.

As we know, the electric potential on an equipotential surface is constant at every point, this means the potential difference between any two points is zero. 

Work-Potential relation: W=qΔV 

Since, ΔV = 0 

W = 0 

Read More: NCERT Solution for Class 11 & 12

The electric field and potential are related by the rate of change of potential with respect to distance. 

 Mathematical Relation 

1. In one dimension

E= −dV / dx 

 The electric field at a point on an equipotential surface is equal to the negative gradient of the electric potential in that direction. 

2. In vector form (3D)

$\stackrel{\to }{E}=-\nabla V$

 Where ∇V (gradient of potential) gives the direction and rate of maximum change. 

 Key point: 

•  The electric field is strong if the potential changes rapidly with distance. 

• In an equipotential surface, if the potential is constant, the electric field is zero.

Recommended Topics: 

Students can check here the properties of an equipotential surface.

1. Constant Potential:

• Electric potential is the same at all points. 

• The potential difference is zero at any point. 

2. Zero Work Done:

• No work is required to move a charge on an equipotential surface. 

3. Perpendicular to Electric Field:

• The electric field intersects the equipotential surface at a right angle. 

• This prevents any component of the electric field along the surface. 

4. Shape Depends on Charge Distribution:

• The surface is a concentric sphere for a point charge. 

• Parallel equipotential surface for a uniform electric field. 

• For the line of charge, it is cylindrical. 

5. Closer Surface:

• The electric field is stronger when the equipotential surfaces. 

• A larger gap means a weaker field.