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.
Consider the following statements about charged conductors:
(A) The electric field inside a charge-free cavity of a conductor is zero, whatever the field outside.
(B) When a conductor with an empty cavity is charged, part of the charge sits on the surface of the cavity.
(C) Just outside a charged conductor, the field has magnitude \(\sigma/\varepsilon_0\), where \(\sigma\) is the surface charge density there.
(D) At the surface of a charged conductor, the electric field points outward whatever the sign of the charge.
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → (A) and (C) only
In the static situation, the field inside the metal of a conductor is zero. This decides where its charges go and how the field behaves at its surface.
(A) The electric field inside a charge-free cavity of a conductor is zero, whatever the field outside. — True. This is electrostatic shielding. The cavity is shielded from all charges and fields outside the conductor.
(B) When a conductor with an empty cavity is charged, part of the charge sits on the surface of the cavity. — False. With no charge in the cavity, all the charge resides on the outer surface of the conductor.
(C) Just outside a charged conductor, the field has magnitude \(\sigma/\varepsilon_0\), where \(\sigma\) is the surface charge density there. — True. A small pill box across the surface encloses charge \( \sigma\,\delta S \), and only its outer face has flux. Gauss’s law then gives \( E=\sigma/\varepsilon_0 \).
(D) At the surface of a charged conductor, the electric field points outward whatever the sign of the charge. — False. The field is outward along the normal only for \( \sigma\gt0 \). For \( \sigma\lt0 \) it points inward.
NCERT (2026-27):
Electrostatics of Conductors – “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.”
Electrostatics of Conductors – “A related result is that even if the conductor … is charged or charges are induced on a neutral conductor by an external field, all charges reside only on the outer surface of a conductor with cavity.”
Electrostatics of Conductors – “By Gauss’s law”
\( \displaystyle E\,\delta S=\frac{\sigma\,\delta S}{\varepsilon_0} \quad \)\( \displaystyle E=\frac{\sigma}{\varepsilon_0} \)\( \qquad (2.36) \)
Electrostatics of Conductors – “For σ > 0, electric field is normal to the surface outward; for σ < 0, electric field is normal to the surface inward.”