The magnetic dipole moment has the dimension of

Options

A. current x length
B. charge x time x length
C. current x area
D. `("current")/("area")`

Explanation

To determine the dimension of the magnetic dipole moment, we can follow these steps:

### Step 1: Understand the Definition of Magnetic Dipole Moment
The magnetic dipole moment (denoted as \( M \)) is a measure of the strength and orientation of a magnetic source. For a current-carrying loop, it can be defined as:

\[ M = N \cdot I \cdot A \]

where:
- \( N \) = number of turns in the loop
- \( I \) = current flowing through the loop
- \( A \) = area of the loop

### Step 2: Determine the Dimensions of Each Component
1. **Current (I)**: The dimension of electric current is given as:
\[ [I] = [A] \quad \text{(Ampere)} \]

2. **Area (A)**: The area of a loop can be expressed in terms of length:
\[ [A] = [L^2] \quad \text{(Square meter)} \]

### Step 3: Combine the Dimensions
Now, substituting the dimensions into the formula for magnetic dipole moment:

\[ [M] = [N] \cdot [I] \cdot [A] \]

Since \( N \) (number of turns) is a dimensionless quantity, we can ignore it in terms of dimensions. Thus, we have:

\[ [M] = [I] \cdot [A] = [A] \cdot [L^2] \]

### Step 4: Final Dimension of Magnetic Dipole Moment
Combining these dimensions gives:

\[ [M] = [A \cdot L^2] \]

This indicates that the magnetic dipole moment has the dimensions of current multiplied by area.

### Conclusion
The dimension of the magnetic dipole moment is:

\[ \text{Current} \times \text{Area} \quad \text{(Option 3)} \]