Match the following columns.
`{:(,"Column I",,"Column II"),(A.,"Tesla",p,[ML^(2)A^(-2)T^(-2)]),(B.,"Weber",q,[MLA^(-2)T^(-1)]),(C.,"Weber m"^(-2),r.,[MA^(-1)T^(-2)]),(D.,"Henry",s.,"None"):}`

Explanation

To solve the problem of matching the units in Column I with their corresponding dimensions in Column II, we will analyze each unit one by one.

### Step-by-Step Solution:

1. **Match Tesla (A)**:
- Tesla (T) is the unit of magnetic field.
- The formula for the magnetic field (B) is given by:
\[ B = \frac{F}{Q \cdot V} \]
- Where:
- \( F \) (force) has dimensions \( [M^1 L^1 T^{-2}] \)
- \( Q \) (charge) is \( I \cdot T \) (current times time), so its dimensions are \( [A^1 T^1] \)
- \( V \) (velocity) has dimensions \( [L^1 T^{-1}] \)
- Substituting these into the formula:
\[ B = \frac{[M^1 L^1 T^{-2}]}{[A^1 T^1] \cdot [L^1 T^{-1}]} = \frac{[M^1 L^1 T^{-2}]}{[A^1 L^1 T^0]} = [M^1 A^{-1} T^{-2}] \]
- Therefore, Tesla corresponds to **R**: \( [M^1 A^{-1} T^{-2}] \).

2. **Match Weber (B)**:
- Weber (Wb) is the unit of magnetic flux.
- The magnetic flux (Φ) is given by:
\[ Φ = B \cdot A \]
- Where:
- \( B \) has dimensions \( [M^1 A^{-1} T^{-2}] \) (as calculated above)
- \( A \) (area) has dimensions \( [L^2] \)
- Thus, the dimensions for magnetic flux are:
\[ Φ = [M^1 A^{-1} T^{-2}] \cdot [L^2] = [M^1 L^2 A^{-1} T^{-2}] \]
- This matches with **S**: "None" since there is no corresponding match in Column II.

3. **Match Weber m\(^{-2}\) (C)**:
- Weber per square meter (Wb/m²) is equivalent to Tesla (T).
- Therefore, the dimensions are the same as those for Tesla:
\[ [M^1 A^{-1} T^{-2}] \]
- Thus, Weber per square meter also corresponds to **R**.

4. **Match Henry (D)**:
- Henry (H) is the unit of inductance.
- The inductance (L) is given by:
\[ L = \frac{Φ}{I} \]
- Where:
- \( Φ \) has dimensions \( [M^1 L^2 A^{-1} T^{-2}] \) (as calculated for Weber)
- \( I \) (current) has dimensions \( [A^1] \)
- Therefore, the dimensions for inductance are:
\[ L = \frac{[M^1 L^2 A^{-1} T^{-2}]}{[A^1]} = [M^1 L^2 A^{-2} T^{-2}] \]
- This matches with **P**: \( [M^1 L^2 A^{-2} T^{-2}] \).

### Final Matches:
- A (Tesla) → R \([M^1 A^{-1} T^{-2}]\)
- B (Weber) → S (None)
- C (Weber m\(^{-2}\)) → R \([M^1 A^{-1} T^{-2}]\)
- D (Henry) → P \([M^1 L^2 A^{-2} T^{-2}]\)