Electric field \( \vec{E} \) at the surface of charged conductor is:
A. \( |\vec{E}| = \displaystyle\frac{\sigma}{\varepsilon_0} \)
B. \( \vec{E} \) has a tangential component
C. Electric field is zero everywhere inside the conductor.
D. Any excess charge must reside on the surface of the conductor.
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → A, C and D only
In electrostatic equilibrium the free charges in a conductor are at rest, so the field inside is zero and the field just outside has no component along the surface.
(A) \( |\vec{E}| = \sigma/\varepsilon_0 \) — Correct. Gauss's law for a small pillbox across the surface (field zero inside, normal outside) gives \( E\,\Delta S = \sigma\,\Delta S/\varepsilon_0 \).
(B) \( \vec{E} \) has a tangential component — Incorrect. A tangential component would move the free charges along the surface. In equilibrium the field is normal to the surface.
(C) Electric field is zero everywhere inside the conductor. — Correct. Any field inside would drive a current; the free charges rearrange until it is zero.
(D) Any excess charge must reside on the surface of the conductor. — Correct. Gauss's law over any closed surface inside the conductor, where \( E = 0 \), gives zero enclosed charge, so the excess charge sits on the surface.
NCERT (2026-27):
Electrostatics of Conductors – “… 1. Inside a conductor, electrostatic field is zero …
2. At the surface of a charged conductor, electrostatic field must be normal to the surface at every point … In the static situation, therefore, E should have no tangential component. …
3. The interior of a conductor can have no excess charge in the static situation … When the conductor is charged, the excess charge can reside only on the surface in the static situation. …
5. Electric field at the surface of a charged conductor
\( \displaystyle \mathbf{E} = \frac{\sigma}{\varepsilon_0}\,\hat{\mathbf{n}} \qquad (2.35) \)
where σ is the surface charge density and n̂ is a unit vector normal to the surface in the outward direction.”