Dimension of magnetic moment is given by:

Options

A. `[AL^(2)]`
B. `[A^(2)L^(2)]`
C. `[AL^(3)]`
D. Both (a) and (c )

Explanation

To find the dimension of magnetic moment, we start with the formula for magnetic moment (M) given by:

\[ M = n \cdot i \cdot A \]

Where:
- \( n \) is the number of turns in the coil (dimensionless),
- \( i \) is the current (measured in Amperes, A),
- \( A \) is the area of the coil (measured in square meters, m²).

### Step 1: Identify the dimensions of current (i)
The dimension of current (i) is given by:
\[ [i] = [A] \]
Where \( [A] \) represents the dimension of electric current.

### Step 2: Identify the dimensions of area (A)
The area (A) of a circular coil is given by:
\[ A = \pi r^2 \]
The dimension of area is:
\[ [A] = [L^2] \]
Where \( [L] \) represents the dimension of length.

### Step 3: Combine the dimensions
Now, we can combine the dimensions of current and area to find the dimension of magnetic moment:
\[ [M] = [n] \cdot [i] \cdot [A] \]
Since \( n \) is dimensionless:
\[ [M] = [A] \cdot [L^2] \]

Substituting the dimensions:
\[ [M] = [A] \cdot [L^2] = [A^1 L^2] \]

### Conclusion
Thus, the dimension of magnetic moment is:
\[ [M] = [A^1 L^2] \]

### Answer
The dimension of magnetic moment is given by \( [A^1 L^2] \).

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