In the case of a charged conductor with a cavity (with no charge inside the cavity), which of the following options is correct? (where symbols have their usual meaning)
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → Inside the cavity \( E = 0, V = V_0 \) (constant)
In electrostatic equilibrium the field inside the material of a conductor is zero, so the whole conductor, including the wall of the cavity, is at one potential \( V_0 \). A cavity with no charge in it is surrounded by this equipotential surface, so the potential everywhere inside the cavity is the same \( V_0 \), and a potential that does not change from point to point means zero field.
\( V = V_0 \text{ (constant)} \)
\( E = -dV/dr = 0 \)
This is electrostatic shielding: the cavity is free of field whatever the charge on the conductor or the fields outside it.
Why the other options are incorrect
Option (1) Inside the cavity \( E \ne 0, \sigma = 0 \) — Incorrect. No field exists inside a charge-free cavity. (No charge sits on the cavity wall, so \( \sigma = 0 \) there is true, but \( E \ne 0 \) is not.)
Option (2) Inside the cavity \( E = 0, V = 0 \) — Incorrect. Zero field means the potential is constant, not zero. It equals the potential of the conductor, which in general is not zero.
Option (4) Outside the conductor \( E = 0 \) — Incorrect. Outside a charged conductor the field is not zero; just outside its surface it is \( \sigma/\varepsilon_0 \), normal to the surface.
NCERT (2026-27):
Electrostatics of Conductors – “… 4. Electrostatic potential is constant throughout the volume of the conductor and has the same value (as inside) on its surface … That is, there is no potential difference between any two points inside or on the surface of the conductor.”
Electrostatics of Conductors – “… Consider a conductor with a cavity, with no charges inside the cavity. A remarkable result is that the electric field inside the cavity is zero, whatever be the size and shape of the cavity and whatever be the charge on the conductor and the external fields in which it might be placed. … Whatever be the charge and field configuration outside, any cavity in a conductor remains shielded from outside electric influence: the field inside the cavity is always zero. This is known as electrostatic shielding.”