A wire of length `L metre ` , carrying a current `I `ampere is bent in the form of a circle . The magnitude of its magnetic moment is …………. ` MKS units ` .

Options

A. (a)`IL^(2)//2pi`
B. (b)`I^(2)L^(2)//4pi`
C. (c)`IL^(2)//4pi`
D. (d)`IL^(2)//8pi`

Explanation

To find the magnetic moment of a wire of length \( L \) meters carrying a current \( I \) amperes when bent into the form of a circle, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Geometry of the Wire**:
The wire is bent into a circular shape. The length of the wire \( L \) is equal to the circumference of the circle formed by the wire.
\[ L = 2\pi r \]
where \( r \) is the radius of the circle.

2. **Calculate the Radius**:
From the circumference formula, we can express the radius \( r \) in terms of the length \( L \):
\[ r = \frac{L}{2\pi} \]

3. **Determine the Area of the Circle**:
The area \( A \) of the circle can be calculated using the formula:
\[ A = \pi r^2 \]
Substituting the expression for \( r \):
\[ A = \pi \left(\frac{L}{2\pi}\right)^2 = \pi \cdot \frac{L^2}{4\pi^2} = \frac{L^2}{4\pi} \]

4. **Calculate the Magnetic Moment**:
The magnetic moment \( M \) is given by the product of the current \( I \) and the area \( A \):
\[ M = I \cdot A \]
Substituting the expression for \( A \):
\[ M = I \cdot \frac{L^2}{4\pi} \]

5. **Final Expression**:
Thus, the magnetic moment \( M \) of the wire bent in the form of a circle is:
\[ M = \frac{I L^2}{4\pi} \]

### Final Answer:
The magnitude of the magnetic moment in MKS units is:
\[ M = \frac{I L^2}{4\pi} \]