Case: Read the passage and answer the question.
When an excess charge is placed on an isolated conductor, it distributes itself on the surface of that conductor so that all points of the conductor, whether on the surface or inside the conductor, come to the same potential. This is true even if there is a cavity inside the conductor.
If an isolated conductor is placed in an external electric field, all points of the conductor still come to a single potential, regardless of whether the conductor has an excess charge. The free electrons distribute themselves on the surface in such a way that the electric field they produce at interior points cancels the external field that would otherwise be there.
In an electric field, equipotential surfaces must
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → have decreasing potential in the direction of the field
Option (1) be plane surfaces — Incorrect. Equipotential surfaces are planes only in a uniform field. For a single point charge, they are concentric spheres centred at the charge.
Option (2) be tangential to the direction of the field — Incorrect. No work is done in moving a charge on an equipotential surface. So the field has no component along it, and the field is normal to the surface at every point.
Option (3) be spaced such that surfaces having equal difference in potential are separated by equal distances — Incorrect. Since \( E=|\delta V|/\delta l \), surfaces with the same potential difference lie closer together where the field is stronger. Equal spacing holds only in a uniform field.
Option (4) have decreasing potential in the direction of the field — Correct. The electric field points in the direction in which the potential decreases steepest. So, moving along the field, we cross equipotential surfaces of lower and lower potential.
NCERT (2026-27):
Relation Between Field and Potential – “We thus arrive at two important conclusions concerning the relation between electric field and potential: (i) Electric field is in the direction in which the potential decreases steepest.”