When an external electric potential difference \(V\) is applied across two ends of a metallic conductor, then
A. the charge carriers remain static in the conductor, having no motion before applying the potential difference \(V\).
B. the drift velocity in the conductor is the average velocity of free electrons after applying the potential difference \(V\) at the ends of the conductor.
C. the charge carriers experience a force of magnitude \(F = eE\), where \(E\) is electric field produced due to \(V\).
D. the free electrons get accelerated in a direction opposite to \(E\), electric field produced due to \(V\).
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → B, C and D only
The free electrons in a metal are always in random thermal motion; an applied field only adds a small drift opposite to the field.
(A) the charge carriers remain static in the conductor, having no motion before applying the potential difference \( V \). — Incorrect. Even with no potential difference, the free electrons move randomly at high speeds; only their average velocity is zero, so there is no net current.
(B) the drift velocity in the conductor is the average velocity of free electrons after applying the potential difference \( V \) at the ends of the conductor. — Correct. This is the definition of drift velocity, \( v_d = -eE\tau/m \).
(C) the charge carriers experience a force of magnitude \( F = eE \), where \( E \) is electric field produced due to \( V \). — Correct. The field \( E = V/l \) acts on each electron of charge e.
(D) the free electrons get accelerated in a direction opposite to \( E \), electric field produced due to \( V \). — Correct. The electron’s charge is negative, so the force \( -e\vec{E} \) and the acceleration \( -e\vec{E}/m \) are opposite to the field (between collisions).
NCERT (2026-27):
Drift of Electrons and the Origin of Resistivity – “As remarked before, an electron will suffer collisions with the heavy fixed ions, but after collision, it will emerge with the same speed but in random directions. If we consider all the electrons, their average velocity will be zero since their directions are random.”
Drift of Electrons and the Origin of Resistivity – “… Consider now the situation when an electric field is present. Electrons will be accelerated due to this field by
\( \displaystyle \mathbf{a} = \frac{-e\mathbf{E}}{m} \qquad (3.15) \)
where –e is the charge and m is the mass of an electron.”
Drift of Electrons and the Origin of Resistivity – “… It tells us that the electrons move with an average velocity which is independent of time, although electrons are accelerated. This is the phenomenon of drift and the velocity vd in Eq. (3.17) is called the drift velocity.”