Match the LIST-I with LIST-II List-I A. Magnetic induction B. Magnetic flux C. Magnetic permeability D. Self inductance List-II I. MLT⁻²A⁻² II. ML²T⁻²A⁻² III. ML⁰T⁻²A⁻¹ IV. ML²T⁻²A⁻¹ Choose the correct answer from the options given below:

Match the LIST-I with LIST-II for Magnetic induction, Magnetic flux, Magnetic permeability and Self inductance

Q. Match the LIST-I with LIST-II

Choose the correct answer from the options given below:

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

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

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

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

Explanation (Dimensional Analysis)

Magnetic induction \(B\) is given by force per unit current per unit length:

\[ B = \frac{F}{IL} \]

\[ [B] = \frac{MLT^{-2}}{AL} = ML^{0}T^{-2}A^{-1} \]

So, Magnetic induction → III.

Magnetic flux \(\Phi\) is given by:

\[ \Phi = BA \]

\[ [\Phi] = (ML^{0}T^{-2}A^{-1})(L^{2}) = ML^{2}T^{-2}A^{-1} \]

So, Magnetic flux → IV.

Magnetic permeability \(\mu\) is defined as:

\[ \mu = \frac{B}{H} \]

Since magnetic field intensity \(H\) has dimension \(AT^{-1}L^{-1}\),

\[ [\mu] = \frac{ML^{0}T^{-2}A^{-1}}{AL^{-1}} = MLT^{-2}A^{-2} \]

So, Magnetic permeability → I.

Self inductance \(L\) is defined by:

\[ E = L \frac{dI}{dt} \]

\[ [L] = \frac{ML^{2}T^{-3}A^{-1}}{AT^{-1}} = ML^{2}T^{-2}A^{-2} \]

So, Self inductance → II.

Hence, the correct matching is:

\[ \boxed{A\text{-}III,\; B\text{-}IV,\; C\text{-}I,\; D\text{-}II} \]