The dimensions of magnetic flux are

Options

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

Explanation

To find the dimensions of magnetic flux, we can follow these steps:

### Step 1: Understand the Definition of 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:
\[ \Phi = B \cdot A \]

### Step 2: Determine the Dimensions of Magnetic Field (B)
To find the dimensions of magnetic flux, we first need the dimensions of the magnetic field (B). We can use the formula for the magnetic force on a charge moving in a magnetic field:
\[ F = Q (v \times B) \]
Where:
- \( F \) = force
- \( Q \) = charge
- \( v \) = velocity
- \( B \) = magnetic field

From this equation, we can express the dimensions of the magnetic field (B):
\[ [F] = [Q] \cdot [v] \cdot [B] \]
Rearranging gives:
\[ [B] = \frac{[F]}{[Q] \cdot [v]} \]

### Step 3: Substitute Dimensions
Now we substitute the dimensions of force, charge, and velocity:
- The dimensional formula for force \( [F] \) is \( [M L T^{-2}] \).
- The dimensional formula for charge \( [Q] \) is \( [I T] \) (where \( I \) is current).
- The dimensional formula for velocity \( [v] \) is \( [L T^{-1}] \).

Substituting these into the equation for \( B \):
\[ [B] = \frac{[M L T^{-2}]}{[I T] \cdot [L T^{-1}]} \]
This simplifies to:
\[ [B] = \frac{M L T^{-2}}{I L T^{-1}} = \frac{M}{I T} \]

### Step 4: Find Dimensions of Area (A)
The area (A) has the dimensional formula:
\[ [A] = [L^2] \]

### Step 5: Combine to Find Dimensions of Magnetic Flux (Φ)
Now we can find the dimensions of magnetic flux:
\[ [\Phi] = [B] \cdot [A] \]
Substituting the dimensions we found:
\[ [\Phi] = \left(\frac{M}{I T}\right) \cdot [L^2] \]
This gives:
\[ [\Phi] = \frac{M L^2}{I T} \]

### Step 6: Final Expression
Thus, the final dimensional formula for magnetic flux is:
\[ [\Phi] = M L^2 T^{-2} I^{-1} \]

### Conclusion
The dimensions of magnetic flux are:
\[ [M L^2 T^{-2} I^{-1}] \]