Question

If a uniform electric field exists in a region of space, is the potential the same at all points in the region? Explain.

 

 

Answer 1

The electric potential V due to a point charge Q at a distance r is given as follows:

V = k Q/r

 

The electric field E due to a point charge Q at a distance r is given as follows:

E = k Q/r2

 

Here, k is Coulombs constant.

 

Rearrange the above equation E = k Q/r2 as follows:

Er = k Q/r

 

Substitute Er for kQ/r in the above equation V = kQ/r, and solve for V.

V = Er

 

Since the field E is uniform in a region of space, it must be constant at any point in the region.

E = constant

 

For constant field E, the potential V is directly proportional to distance r.

V α r

 

Use above relation V α r, electric potential V changes linearly with distance r.

Thus, the electric potential is not same at all points in the region.

Thus, the electric potential is not same at all points in the region.