Choose the correct option:
In a region of constant potential
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → There can be no charge inside the region and the electric field is zero
The electric field is the negative potential gradient, \( E = -\frac{dV}{dr} \). If the potential is constant throughout a region, then \( dV = 0 \) and the field is zero there.
A zero field means that the flux through every closed surface inside the region is zero, so by Gauss's law no charge is enclosed. Hence there can be no charge inside the region.
Why the other options are incorrect
Option (1) There is charge inside the region — Incorrect. Charge inside would give a non-zero field, and then the potential could not be constant.
Option (2) The electric field is uniform — Incorrect as an answer. A uniform non-zero field would make the potential change linearly with distance. The field in a region of constant potential is zero, which is what Option (3) states completely.
Option (4) The electric field shall necessarily change on placing a charge outside the region — Incorrect. The word “necessarily” fails: inside a conductor, for example, the free charges rearrange so that the field stays zero.
NCERT Exemplar:
Electrostatic Potential and Capacitance – …
