Question

A circular loop is made from a wire of length 6m. If 2A current passes through the circular loop, what is the magnetic moment of the loop?

Hint:

The magnetic moment of a circular loop depends on both the current and the area of the loop. The area can be found from the length of the wire.

Answer 1

Step 1: Use the formula for the magnetic moment.
The magnetic moment \( M \) of a current-carrying loop is given by: \[ M = I \times A \] where:
- \( I \) is the current,
- \( A \) is the area of the loop.

Step 2: Calculate the area of the loop.
The wire forms a circular loop, so the circumference of the loop is equal to the length of the wire. The circumference is: \[ C = 2 \pi r \] where \( r \) is the radius of the loop. Since the total length of the wire is 6m: \[ 2 \pi r = 6 \quad \Rightarrow \quad r = \frac{6}{2 \pi} = \frac{3}{\pi} \, \text{m} \] Now, calculate the area \( A \) of the circle: \[ A = \pi r^2 = \pi \left( \frac{3}{\pi} \right)^2 = \frac{9}{\pi} \, \text{m}^2 \]
Step 3: Calculate the magnetic moment.
Now, substitute the current \( I = 2 \, \text{A} \) and the area \( A = \frac{9}{\pi} \) into the formula for magnetic moment: \[ M = 2 \times \frac{9}{\pi} = \frac{18}{\pi} \, \text{A} \cdot \text{m}^2 \] Thus, the magnetic moment of the loop is: \[ \boxed{\frac{18}{\pi} \, \text{A} \cdot \text{m}^2} \]