The dimensional formula for planck's magnetic flux is

Options

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

Explanation

To find the dimensional formula for Planck's magnetic flux, we start with the definition of magnetic flux and the relationship between magnetic field, force, current, and length.

### 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. **Using Lorentz Force**:
The Lorentz force equation relates the magnetic field (B) to force (F), current (I), and length (l):
\[ F = B \cdot I \cdot l \]
From this, we can express the magnetic field (B) as:
\[ B = \frac{F}{I \cdot l} \]

3. **Substituting B into the Magnetic Flux Formula**:
Now, substituting the expression for B into the magnetic flux formula:
\[ Φ = \left(\frac{F}{I \cdot l}\right) \cdot A \]

4. **Expressing Area (A)**:
The area (A) can be expressed in terms of length:
\[ A = l^2 \]

5. **Combining the Equations**:
Substituting A into the magnetic flux equation gives:
\[ Φ = \frac{F \cdot l^2}{I \cdot l} = \frac{F \cdot l}{I} \]

6. **Finding Dimensions**:
Now we need to find the dimensions of each term:
- Force (F) has the dimensions of mass (M), length (L), and time (T):
\[ [F] = M L T^{-2} \]
- Current (I) has the dimensions of electric current:
\[ [I] = A \]
- Length (l) has the dimensions of length:
\[ [l] = L \]

7. **Putting it All Together**:
Now substituting the dimensions into the magnetic flux formula:
\[ [Φ] = \frac{M L T^{-2} \cdot L}{A} = \frac{M L^2 T^{-2}}{A} \]

8. **Final Dimensional Formula**:
Thus, the dimensional formula for Planck's magnetic flux is:
\[ [Φ] = M L^2 T^{-2} A^{-1} \]

### Conclusion:
The dimensional formula for Planck's magnetic flux is \( M L^2 T^{-2} A^{-1} \).