Question

In a region of constant potential:
A. The electric field is uniform.
B. The electric field is zero.
C. There can be no charge inside the region.
D. Both (B) and (C) are correct.

Answer 1

Hint: The electric field is the negative differentiation of potential with respect to the small displacement dx. We know that charge produces electric fields. If there is an electric field in that region, there should be charges present in the region.

Complete answer:
To answer this question, we use the relation between electric potential and electric field.
The electric field in the region of potential difference is expressed as,
\[E = - \dfrac{{dV}}{{dx}}\] ……. (1)
Here, \[dV\] is the potential difference and \[dx\] is the small displacement.

We have given that the potential is constant in the given region. Therefore,
\[V = {\text{constant}}\]
The electric field will be uniform in the given region if and only if there is linear change in potential with the distance x. Since the potential does not change. The electric field cannot be uniform. Therefore, the option (A) is incorrect.

Since V is constant, the electric field,
\[E = - \dfrac{{dV}}{{dx}} = 0\]
Therefore, the electric field in this region is zero. We know that charge produces electric fields. Since there is no electric field in the given region, we can say there are no any charges in the region.

So, the correct answer is option (B) and (C).

Note: Equation (1) is obtained from expression of work done to move the point charge in the potential difference. The work done to move the unit charge is equal to potential difference between two points. The negative sign in the above equation denotes that we are moving the charge against the electric force acting on it.