Match the LIST-I with LIST-II (Symbols have their usual meaning)
| LIST-I (Physical Quantity) | LIST-II (Expression) | ||
|---|---|---|---|
| A. | Potential energy of a dipole in a uniform electric field | I. | \( q[\vec{v}\times\vec{B}] \) |
| B. | Torque on an electric dipole in a uniform electric field | II. | \( \vec{m}\times\vec{B} \) |
| C. | Force on a charged particle in a uniform magnetic field | III. | \( \vec{p}\times\vec{E} \) |
| D. | Torque on a magnetic dipole in a uniform magnetic field | IV. | \( -\vec{p}\cdot\vec{E} \) |
[Symbols have their usual meaning]
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → A-IV, B-III, C-I, D-II
Each expression follows from the definition of the quantity: a dot product gives a scalar (energy), while a cross product gives a vector (force or torque).
(A) Potential energy of a dipole in a uniform electric field — this matches (IV) \( -\vec{p}\cdot\vec{E} \). It is the work done in turning the dipole from the position perpendicular to the field, \( U = -pE\cos\theta \).
(B) Torque on an electric dipole in a uniform electric field — this matches (III) \( \vec{p}\times\vec{E} \). The two equal and opposite forces \( \pm q\vec{E} \) form a couple of magnitude \( pE\sin\theta \).
(C) Force on a charged particle in a uniform magnetic field — this matches (I) \( q[\vec{v}\times\vec{B}] \). This is the magnetic part of the Lorentz force.
(D) Torque on a magnetic dipole in a uniform magnetic field — this matches (II) \( \vec{m}\times\vec{B} \). A current loop or bar magnet of moment \( \vec{m} \) behaves exactly like an electric dipole with \( \vec{p} \to \vec{m} \) and \( \vec{E} \to \vec{B} \).
NCERT (2026-27):
Summary – “… The potential energy of a dipole moment p in a uniform electric field E is \( -\mathbf{p}\cdot\mathbf{E} \).”
Summary – “… 13. In a uniform electric field E, a dipole experiences a torque \( \boldsymbol{\tau} \) given by \( \boldsymbol{\tau} = \mathbf{p}\times\mathbf{E} \) but experiences no net force.”
Magnetic Field, Lorentz Force – “… (ii) The magnetic force \( q[\mathbf{v}\times\mathbf{B}] \) includes a vector product of velocity and magnetic field.”
Summary – “… 2. When a bar magnet of dipole moment m is placed in a uniform magnetic field B, (a) the force on it is zero, (b) the torque on it is \( \mathbf{m}\times\mathbf{B} \), (c) its potential energy is \( -\mathbf{m}\cdot\mathbf{B} \), where we choose the zero of energy at the orientation when m is perpendicular to B.”