Chapter 20, Problem 1CQ

In one region of space the electric potential has a positive constant value. In another region of space the potential has a negative constant value. What can be said about the electric field within each of these two regions of space?

To determine

The electric field in each of the two given region of space.

Answer to Problem 1CQ

The electric field in both of the region is zero because the electric potential is constant in both the regions and the gradient of any constant quantity is zero.

Explanation of Solution

Write the expression for the electric field.

$E=-\frac{\Delta V}{\Delta s}$

Here,

$E$ is the electric field at any point.

$\Delta V$ is the change in electric potential.

$\Delta s$ is the change in the distance.

The gradient of a constant quantity is zero. So, when the electric potential in a region is constant then the electric field at that region is zero.

It is given that the electric potential in one region is positive constant value and in another region is negative constant value. So, the gradient of the electric potential is zero in both the region. Thus the electric field is zero in both the region.

Conclusion:

Therefore, the electric field in both of the region is zero because the electric potential is constant in both the regions and the gradient of any constant quantity is zero.