The magnetic flux has the dimension

Options

A. `M L^(2) T A^(-1)`
B. `M L^(2) T^(-1) A^(-1)`
C. `M T^(-2) A^(-1)`
D. `M L^(2) T^(-2) A^(-1)`

Answer

To determine the dimension of magnetic flux, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding Magnetic Flux**:
Magnetic flux (Φ) is defined as the product of the magnetic field (B) and the area (A) through which the field lines pass. Mathematically, it can be expressed as:
\[ Φ = B \cdot A \]

2. **Finding the Dimension of Magnetic Field (B)**:
The magnetic field can be derived from the formula for force (F) on a current-carrying conductor:
\[ F = I \cdot L \cdot B \]
Rearranging this gives:
\[ B = \frac{F}{I \cdot L} \]

3. **Substituting Dimensions**:
- The dimension of force (F) is given by:
\[ [F] = M L T^{-2} \]
- The dimension of current (I) is:
\[ [I] = A \]
- The dimension of length (L) is:
\[ [L] = L \]

4. **Combining Dimensions**:
Substituting the dimensions into the equation for B:
\[ [B] = \frac{[F]}{[I] \cdot [L]} = \frac{M L T^{-2}}{A \cdot L} \]
Simplifying this gives:
\[ [B] = \frac{M T^{-2}}{A} \]

5. **Finding the Dimension of Area (A)**:
The dimension of area is:
\[ [A] = L^2 \]

6. **Calculating the Dimension of Magnetic Flux (Φ)**:
Now, substituting the dimensions of B and A into the equation for magnetic flux:
\[ [Φ] = [B] \cdot [A] = \left(\frac{M T^{-2}}{A}\right) \cdot (L^2) \]
This results in:
\[ [Φ] = M L^2 A^{-1} T^{-2} \]

7. **Final Result**:
Therefore, the dimension of magnetic flux is:
\[ [Φ] = M L^2 A^{-1} T^{-2} \]

### Conclusion:
Among the options provided, the correct answer for the dimension of magnetic flux is \( M L^2 A^{-1} T^{-2} \).

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