Match List-I with List-II. List-I List-II (A) Magnetic field (I)...

To find the dimensional formulas, we use standard relations:

(A) Magnetic field ($B$): From the magnetic force $F = qvB$, we have $[B] = \dfrac{[F]}{[q][v]} = \dfrac{[MLT^{-2}]}{[AT][LT^{-1}]} = [MT^{-2}A^{-1}]$. Thus, A matches with IV.

(B) Magnetic flux ($\Phi$): From $\Phi = BA$, we have $[\Phi] = [MT^{-2}A^{-1}][L^2] = [ML^2T^{-2}A^{-1}]$. Thus, B matches with III.

(C) Magnetic permeability ($\mu_0$): From the force per unit length between parallel wires $\dfrac{F}{L} = \dfrac{\mu_0 I_1 I_2}{2\pi r}$, we have $[\mu_0] = \dfrac{[F][r]}{[L][I^2]} = \dfrac{[MLT^{-2}][L]}{[L][A^2]} = [MLT^{-2}A^{-2}]$. Thus, C matches with II.

(D) Electric permittivity ($\varepsilon_0$): From Coulomb's law $F = \dfrac{1}{4\pi\varepsilon_0}\dfrac{q_1 q_2}{r^2}$, we have $[\varepsilon_0] = \dfrac{[q^2]}{[F][r^2]} = \dfrac{[A^2T^2]}{[MLT^{-2}][L^2]} = [M^{-1}L^{-3}T^4A^2]$. Thus, D matches with I.

The correct matching is (A)-(IV), (B)-(III), (C)-(II), (D)-(I).

Answer: (A)-(IV), (B)-(III), (C)-(II), (D)-(I)