Match List - I with List – II
`{:("List - I","List - II"),("(A) Magnetic Induction", (ii) ML^(2)T^(-2)A^(-1)),("(B) Magnetic Flux", (ii) M^0L^(-1)A),("(C) Magnetic permeability",(iii)MT^(-2)A^(-1)),("(D) Magnetization ",(iv) MLT^(-2) A^(-2)):}`
Choose the most appropriate answer from the options given below

Options

A. (A)-(iii), (B)-(ii), (C)-(iv), (D)-(i)
B. (A)-(iii), (B)-(i), (C)-(iv), (D)-(ii)
C. (A)-(ii), (B)-(iv), (C)-(i), (D)-(iii)
D. (A)-(ii), (B)-(i), (C)-(iv), (D)-(iii)

Explanation

To solve the problem of matching List - I with List - II, we will derive the dimensional formulas for each of the magnetic quantities in List - I and then match them with their corresponding formulas in List - II.

### Step-by-Step Solution:

1. **Magnetic Induction (B)**:
- The formula for the magnetic induction \( B \) can be derived from the force on a current-carrying wire in a magnetic field:
\[ F = I \cdot L \cdot B \]
- Rearranging gives:
\[ B = \frac{F}{I \cdot L} \]
- The dimensions of force \( F \) are \( MLT^{-2} \), current \( I \) has dimensions \( A \), and length \( L \) has dimensions \( L \).
- Therefore, substituting these into the equation gives:
\[ B = \frac{MLT^{-2}}{A \cdot L} = \frac{MT^{-2}}{A} \]
- Thus, the dimensional formula for magnetic induction \( B \) is:
\[ [B] = MT^{-2}A^{-1} \]
- This matches with option (iii) in List - II.

2. **Magnetic Flux (Φ)**:
- The formula for magnetic flux \( Φ \) is given by:
\[ Φ = B \cdot S \]
- Where \( S \) is the area. The dimensions of area \( S \) are \( L^2 \).
- Substituting the dimensions of \( B \):
\[ Φ = (MT^{-2}A^{-1}) \cdot (L^2) = M L^2 T^{-2} A^{-1} \]
- Thus, the dimensional formula for magnetic flux \( Φ \) is:
\[ [Φ] = ML^2T^{-2}A^{-1} \]
- This matches with option (i) in List - II.

3. **Magnetic Permeability (μ)**:
- The magnetic permeability \( μ \) is defined as:
\[ μ = \frac{B}{H} \]
- We already have \( B \) and need to find \( H \) (magnetic field strength). The dimensions of \( H \) are:
\[ H = \frac{B}{μ} \]
- The dimensions of \( H \) are \( A L^{-1} \).
- Substituting the dimensions of \( B \):
\[ μ = \frac{MT^{-2}A^{-1}}{A L^{-1}} = \frac{MT^{-2}}{A^2} \]
- Thus, the dimensional formula for magnetic permeability \( μ \) is:
\[ [μ] = ML^{-1}T^{-2}A^{-2} \]
- This matches with option (iv) in List - II.

4. **Magnetization (M)**:
- The magnetization \( M \) is defined as:
\[ M = \frac{magnetic \ dipole \ moment}{volume} \]
- The dimensions of magnetic dipole moment are \( A L^2 \) and volume is \( L^3 \).
- Thus, the dimensions of magnetization are:
\[ M = \frac{A L^2}{L^3} = A L^{-1} \]
- Thus, the dimensional formula for magnetization \( M \) is:
\[ [M] = A L^{-1} \]
- This matches with option (ii) in List - II.

### Final Matching:
- (A) Magnetic Induction → (iii) \( MT^{-2}A^{-1} \)
- (B) Magnetic Flux → (i) \( ML^2T^{-2}A^{-1} \)
- (C) Magnetic Permeability → (iv) \( ML^{-1}T^{-2}A^{-2} \)
- (D) Magnetization → (ii) \( A L^{-1} \)

### Answer:
The correct matches are:
- A → iii
- B → i
- C → iv
- D → ii