Question

A regular hexagon of side \( m \), which is a wire of length 24 m, is coiled on that hexagon. If current in hexagon is \( I \), then the magnetic moment is 

• A. \( 6\sqrt{3} I \, \text{m}^2 \)
• B. \( 3\sqrt{3} I \, \text{m}^2 \)
• C. \( 3\sqrt{2} I \, \text{m}^2 \)
• D. \( 6 I \, \text{m}^2 \)

Hint:

For regular polygon coils, use the area formula for the polygon and multiply by the current to find the magnetic moment.

Answer 1

The Correct Option is A

The magnetic moment of a current-carrying coil is given by: \[ \mu = I \cdot A \] where \( A \) is the area enclosed by the coil. For a regular hexagon, the area is: \[ A = \frac{3\sqrt{3}}{2} \cdot m^2 \] Thus, the magnetic moment is: \[ \mu = I \cdot \frac{3\sqrt{3}}{2} \cdot m^2 = 6\sqrt{3} I \, \text{m}^2 \] Thus, the correct answer is (A).