Match List-I with List-II
| List-I | List-II |
| (Physical Quantity) | (Units) |
| (A) Magnetic field | (I) \( \mathrm{J\,T^{-1}} \) |
| (B) Magnetic moment | (II) \( \mathrm{T\,m\,A^{-1}} \) |
| (C) Pole strength | (III) \( \mathrm{J\,T^{-1}\,m^{-1}} \) |
| (D) Permeability of free space | (IV) \( \mathrm{Wb\,m^{-2}} \) |
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → (A) - (IV), (B) - (I), (C) - (III), (D) - (II)
Each quantity is matched with its unit from the defining relation.
(A) Magnetic field — this matches (IV) \( \mathrm{Wb\,m^{-2}} \). The field is the magnetic flux per unit area, so its unit is weber per square metre, which is the tesla.
(B) Magnetic moment — this matches (I) \( \mathrm{J\,T^{-1}} \). The energy of a dipole is \( U = -MB\cos\theta \), so \( M = U/B \) has the unit joule per tesla.
(C) Pole strength — this matches (III) \( \mathrm{J\,T^{-1}\,m^{-1}} \). Since \( M = m \times 2l \), the pole strength is \( m = M/2l \), which is joule per tesla per metre (the same as \( \mathrm{A\,m} \)).
(D) Permeability of free space — this matches (II) \( \mathrm{T\,m\,A^{-1}} \). From \( B = \mu_0 I/2\pi r \), \( \mu_0 = 2\pi r B/I \), so its unit is tesla metre per ampere.