Question

A wire of length 4.4 m is bent round in the shape of a circular loop and carries a current of 1.0 A. The magnetic moment of the loop will be:

• A. \( 0.7 \, \text{Am}^2 \)
• B. \( 1.54 \, \text{Am}^2 \)
• C. \( 2.10 \, \text{Am}^2 \)
• D. \( 3.5 \, \text{Am}^2 \)

Hint:

The magnetic moment of a circular loop is the product of the current and the area. Use the circumference to find the radius of the loop.

Answer 1

The Correct Option is B

The magnetic moment \( M \) of a current-carrying loop is given by: \[ M = I A, \] where \( I \) is the current and \( A \) is the area of the loop. The area of a circular loop is: \[ A = \pi r^2. \] The circumference of the loop is \( 2\pi r = 4.4 \, \text{m} \), so: \[ r = \frac{4.4}{2\pi} = 0.7 \, \text{m}. \] Now, calculating the area: \[ A = \pi (0.7)^2 = 1.54 \, \text{m}^2. \] Thus, the magnetic moment is: \[ M = 1.0 \times 1.54 = 1.54 \, \text{Am}^2. \]