Question

Match List I with List II Choose the correct answer from the options given below :

• A. A-I, B-III, C-II, D-IV
• B. A-IV, B-III, C-II, D-I
• C. A-III, B-I, C-II, D-IV
• D. A-IV, B-II, C-III, D-I

Answer 1

Answer: (B)

A-IV, B-III, C-II, D-I

Answer 2

The equations and dimensional analysis are as follows:

The torque ($\tau$) is given by: $\tau = \mathbf{r} \times \mathbf{F} \implies [\tau] = [ML^2T^{-2}]$

The magnetic field ($\mathbf{B}$) is derived as: $\mathbf{F} = [q \mathbf{v} \times \mathbf{B}] \implies [\mathbf{B}] = \frac{[\mathbf{F}]}{[q][\mathbf{v}]} = \frac{MLT^{-2}}{ATL^{-1}} = [MA^{-1}T^{-2}]$

The magnetic moment ($\mathbf{M}$) has the dimensions: $[\mathbf{M}] = [\mathbf{I} \times \mathbf{A}] = [AL^2]$

Using Biot-Savart's Law: $B = \frac{\mu_0 I dl \sin \theta}{r^2}$

The permeability of free space ($\mu$) is derived as: $\mu = \frac{B r^2}{I dl} \implies \mu = \frac{MT^{-2}A^{-1} \times L^2}{AL} = [MLT^{-2}A^{-2}]$

Thus, the correct matching is:

• Torque $\to [ML^2T^{-2}]$
• Magnetic field $\to [MA^{-1}T^{-2}]$
• Magnetic moment $\to [AL^2]$
• Permeability of free space $\to [MLT^{-2}A^{-2}]$