The dimensional formula for Magnetic Moment of a magnet is

Options

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

Answer

To find the dimensional formula for the magnetic moment of a magnet, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding Magnetic Moment**:
The magnetic moment (M) of a magnet can be expressed in terms of the current (I) flowing through a loop and the area (A) of that loop. The formula is given as:
\[ M = n \cdot I \cdot A \]
where \( n \) is the number of turns in the coil.

2. **Identifying Dimensions**:
- The number of turns \( n \) is a dimensionless quantity, so it does not contribute to the dimensional formula.
- The current \( I \) has a unit of Ampere (A).
- The area \( A \) can be expressed in terms of length. Since area is length squared, its unit is \( \text{m}^2 \).

3. **Writing the Units**:
- The unit of current \( I \) is \( \text{A} \).
- The unit of area \( A \) is \( \text{m}^2 \).

4. **Combining the Units**:
The magnetic moment can thus be expressed in terms of its units:
\[ M = I \cdot A = \text{A} \cdot \text{m}^2 \]

5. **Expressing in Dimensional Form**:
- The dimensional formula for current \( I \) is \( [I] = A \).
- The dimensional formula for area \( A \) is \( [A] = L^2 \).
Therefore, the dimensional formula for magnetic moment \( M \) is:
\[ [M] = [I] \cdot [A] = A \cdot L^2 \]

6. **Final Dimensional Formula**:
To express this in standard dimensional notation, we have:
\[ [M] = M^0 \cdot A^1 \cdot L^2 \cdot T^0 \]
This means the dimensional formula for the magnetic moment of a magnet is:
\[ M^0 A^1 L^2 T^0 \]

### Conclusion:
The dimensional formula for the magnetic moment of a magnet is:
\[ M^0 A^1 L^2 T^0 \]