A wire of length 2 m carrying a current of 1 A is bend to form a circle. The magnetic moment of the coil is (in `Am^(2)`)

Options

A. `2pi`
B. `pi//2`
C. `pi//4`
D. `1//pi`

Answer

To find the magnetic moment of a circular coil formed by bending a wire of length 2 m carrying a current of 1 A, we can follow these steps:

### Step 1: Determine the radius of the circle
The length of the wire is equal to the circumference of the circle formed when the wire is bent. The formula for the circumference \( C \) of a circle is given by:

\[ C = 2\pi r \]

where \( r \) is the radius of the circle. Given that the length of the wire \( L = 2 \, \text{m} \), we can set up the equation:

\[ 2 = 2\pi r \]

### Step 2: Solve for the radius \( r \)
Rearranging the equation to solve for \( r \):

\[ r = \frac{2}{2\pi} = \frac{1}{\pi} \, \text{m} \]

### Step 3: Calculate the area \( A \) of the circular loop
The area \( A \) of a circle is given by the formula:

\[ A = \pi r^2 \]

Substituting the value of \( r \):

\[ A = \pi \left(\frac{1}{\pi}\right)^2 = \pi \cdot \frac{1}{\pi^2} = \frac{1}{\pi} \, \text{m}^2 \]

### Step 4: Calculate the magnetic moment \( M \)
The magnetic moment \( M \) of a coil is given by the formula:

\[ M = I \times A \]

where \( I \) is the current flowing through the wire. Given \( I = 1 \, \text{A} \):

\[ M = 1 \times \frac{1}{\pi} = \frac{1}{\pi} \, \text{Am}^2 \]

### Final Answer
The magnetic moment of the coil is:

\[ M = \frac{1}{\pi} \, \text{Am}^2 \]

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