The dimensional formula for magnetic flux is

Options

A. `["ML"^(2)"T"^(-2)"A"^(-1)]`
B. `["ML"^(3)"T"^(-2)"A"^(-2)]`
C. `["M"^(0)"L"^(-2)"T"^(-2)"A"^(-2)]`
D. `["ML"^(2)"T"^(-1)"A"^(2)]`

Explanation

To find the dimensional formula for magnetic flux, we will follow a systematic approach.

### Step-by-Step Solution:

1. **Understanding Magnetic Flux**:
Magnetic flux (Φ_B) is defined as the product of the magnetic field (B) and the area (A) through which the magnetic field lines pass, adjusted by the cosine of the angle (θ) between the magnetic field and the normal to the surface. The formula is given by:
\[ Φ_B = B \cdot A \cdot \cos(θ) \]
Since cos(θ) is dimensionless, we can ignore it for dimensional analysis.

2. **Dimensional Formula of Area (A)**:
The area is defined as length squared. Therefore, the dimensional formula for area is:
\[ [A] = L^2 \]

3. **Finding the Dimensional Formula of Magnetic Field (B)**:
To find the dimensional formula of the magnetic field, we can use the relationship between force (F), charge (q), and velocity (v). The magnetic force on a charged particle moving in a magnetic field is given by:
\[ F = q(v \times B) \]
Rearranging gives:
\[ B = \frac{F}{q \cdot v} \]
Now, we need the dimensional formulas for force, charge, and velocity.

- **Dimensional Formula of Force (F)**:
\[ [F] = M L T^{-2} \]

- **Dimensional Formula of Charge (q)**:
Charge can be expressed in terms of current (I) and time (t):
\[ [q] = I \cdot T \]
In terms of dimensions, current has the dimension:
\[ [I] = A \quad \text{(Ampere)} \]
Thus,
\[ [q] = A T \]

- **Dimensional Formula of Velocity (v)**:
Velocity is defined as distance over time:
\[ [v] = L T^{-1} \]

Now substituting these into the formula for B:
\[ [B] = \frac{[F]}{[q] \cdot [v]} = \frac{M L T^{-2}}{(A T)(L T^{-1})} \]
Simplifying this gives:
\[ [B] = \frac{M L T^{-2}}{A L T^{-1}} = \frac{M}{A T} \]

4. **Combining the Dimensional Formulas**:
Now we can find the dimensional formula for magnetic flux:
\[ [Φ_B] = [B] \cdot [A] = \left(\frac{M}{A T}\right) \cdot (L^2) \]
This results in:
\[ [Φ_B] = \frac{M L^2}{A T} \]

5. **Final Dimensional Formula**:
The final dimensional formula for magnetic flux is:
\[ [Φ_B] = M L^2 A^{-1} T^{-1} \]

### Conclusion:
The dimensional formula for magnetic flux is:
\[ M^1 L^2 A^{-1} T^{-1} \]