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 can follow these steps:

### Step 1: Understand the formula for magnetic flux
Magnetic flux (Φ) is defined as the product of the magnetic field (B) and the area (A) through which the magnetic field lines pass. Therefore, we can express it as:
\[ Φ = B \times A \]

### Step 2: Identify the dimensions of magnetic field (B)
The magnetic field (B) can be derived from the formula for force (F) acting on a charged particle moving in a magnetic field. The formula is:
\[ F = B \times I \times L \]
where:
- F is the force (in Newtons),
- I is the current (in Amperes),
- L is the length (in meters).

Rearranging this gives us:
\[ B = \frac{F}{I \times L} \]

### Step 3: Write the dimensions for force (F)
The dimensional formula for force (F) is:
\[ [F] = M L T^{-2} \]
where:
- M is mass,
- L is length,
- T is time.

### Step 4: Write the dimensions for area (A)
The area (A) is given by:
\[ A = L^2 \]
So, the dimensional formula for area is:
\[ [A] = L^2 \]

### Step 5: Write the dimensions for current (I)
The dimensional formula for current (I) is:
\[ [I] = A \]
where A represents the unit of electric current (Ampere).

### Step 6: Substitute the dimensions into the formula for magnetic field (B)
Now substituting the dimensions into the expression for B:
\[ [B] = \frac{[F]}{[I][L]} = \frac{M L T^{-2}}{A \times L} \]
This simplifies to:
\[ [B] = \frac{M T^{-2}}{A} \]

### Step 7: Substitute B and A into the magnetic flux formula
Now we can substitute the dimensions of B and A into the formula for magnetic flux:
\[ [Φ] = [B] \times [A] = \left(\frac{M T^{-2}}{A}\right) \times (L^2) \]
This gives us:
\[ [Φ] = \frac{M L^2 T^{-2}}{A} \]

### Step 8: Final expression for the dimensional formula of magnetic flux
Thus, the dimensional formula for magnetic flux (Φ) is:
\[ [Φ] = M L^2 T^{-2} A^{-1} \]

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