Match the LIST-I with LIST-II (Symbols have their usual meaning)
| LIST-I | LIST-II | ||
| Quantity | Expression | ||
| A. | Torque on a magnetic dipole | I. | \( -\vec{m}.\vec{B} \) |
| B. | Magnetic moment of a loop | II. | \( \mu_0 ni \) |
| C. | Magnetic field inside a long solenoid | III. | \( iA \) |
| D. | Potential energy of a magnetic dipole | IV. | \( \vec{m}\times\vec{B} \) |
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → A - IV, B - III, C - II, D - I
All four are standard results for a current loop treated as a magnetic dipole of moment \( \vec{m} \).
(A) Torque on a magnetic dipole — this matches (IV) \( \vec{m}\times\vec{B} \). The torque is the cross product, zero when \( \vec{m} \) is along \( \vec{B} \).
(B) Magnetic moment of a loop — this matches (III) \( iA \). The magnetic moment is current times area, directed along the normal.
(C) Magnetic field inside a long solenoid — this matches (II) \( \mu_0ni \), from Ampere’s circuital law, with \( n \) the number of turns per unit length.
(D) Potential energy of a magnetic dipole — this matches (I) \( -\vec{m}.\vec{B} \); it is least when \( \vec{m} \) is along \( \vec{B} \) (stable equilibrium).