Match List I with List II

 Choose the correct answer from the options given below:

Torque:

Torque is given by force × distance.

$$\tau=r\times F$$

Dimensions of force:

$$[F]=[MLT^{-2}]$$

So,

$$[\tau]=[L]\cdot[MLT^{-2}]=[ML^2T^{-2}]$$

So, Torque → (IV)

Magnetic field:

From Lorentz force,

$$F=qvB$$

$$B=\frac{F}{qv}$$

Now substitute dimensions:

$$[q]=[AT]$$

$$\quad[v]=[LT^{-1}]$$

$$[B]=\frac{MLT^{-2}}{(AT)(LT^{-1})}=[MT^{-2}A^{-1}]$$

So, Magnetic field → (III)

Magnetic moment:

Magnetic moment is given by:

$$μ=IA$$

$$[\mu]=[A]\cdot[L^2]=[L^2A]$$

So, Magnetic moment → (II)

Permeability of free space:

Using relation:

$$B=\mu_0\frac{I}{L}$$

$$\mu_0=\frac{BL}{I}$$

Substitute dimensions:

$$[B]=[MT^{-2}A^{-1}]$$

$$[\mu_0]=\frac{(MT^{-2}A^{-1})\cdot L}{A}=[MLT^{-2}A^{-2}]$$

So, Permeability → (I)

Final matching:

(A)−(IV), (B)−(III), (C)−(II), (D)−(I)