Question

The electric potential is constant in a region.What can you say about the electric field there?

Answer 1

Answer:

The Electric field is defined as the gradient of the electric potential. ... If the electric potential is constant, say 1 V, then there is no direction of greatest increase. Hence the gradient of the electric potential is zero, and the electric field is zero everywhere inside the region of constant electric potential.

Answer 2

Answer:

If the electrical potential is constant in a region, then electric field of that region will be zero.

Explanation:

• In electrostatics, the electric field is the force experienced by a unit positive charge. Electric field is denoted by E.
• Electric potential is defined as the work done to move unit charge against the electric field.
• The electric field due to a point charge is equal to the negative potential gradient due to the point charge.
• The relationship between electric field and electric potential is by:

          $E=-\frac{\big d\big V}{\big d\big r}$

We have given, the electric potential is constant in a region.

Electric potential, V = constant

$\frac{\big d\big V}{\big d\big r} =0$

Therefore, E = 0

Hence, the electric field will be equal to zero, when the electric potential in a region does not change.