Magnetic dipole moment of rectangular loop is

Options

A. Inversely proportional to current in loop
B. Inversely proportional to area of loop
C. Parallel to plane of loop and proportional to area of loop
D. Perpendicular to plane of loop and proportional to area of loop

Answer

To find the magnetic dipole moment of a rectangular loop, we can follow these steps:

### Step 1: Understand the concept of magnetic dipole moment
The magnetic dipole moment (\(m\)) is a vector quantity that represents the strength and direction of a magnetic source. For a current-carrying loop, it depends on the current flowing through the loop and the area enclosed by the loop.

### Step 2: Identify the formula for magnetic dipole moment
The magnetic dipole moment for a rectangular loop can be expressed as:
\[ m = n \cdot I \cdot A \]
where:
- \(m\) = magnetic dipole moment
- \(n\) = number of turns in the loop
- \(I\) = current flowing through the loop
- \(A\) = area of the loop

### Step 3: Calculate the area of the rectangular loop
For a rectangular loop with length \(l\) and width \(w\), the area \(A\) can be calculated as:
\[ A = l \cdot w \]

### Step 4: Substitute the area into the magnetic dipole moment formula
Substituting the area into the formula gives:
\[ m = n \cdot I \cdot (l \cdot w) \]

### Step 5: Determine the direction of the magnetic dipole moment
The direction of the magnetic dipole moment is given by the right-hand rule. If the current flows in a clockwise direction, the magnetic dipole moment points inward (toward the plane of the loop). If the current flows in an anti-clockwise direction, the magnetic dipole moment points outward (away from the plane of the loop).

### Step 6: Conclusion
Thus, the magnetic dipole moment of a rectangular loop is given by:
\[ m = n \cdot I \cdot A \]
and it is perpendicular to the plane of the loop.