Question

A circular and a square coil is prepared from two identical metal wires and a current is passed through them. Ratio of magnetic dipole moment associated with circular coil to that with square coil is

• A. \( \frac{\pi}{2} \)
• B. \( \frac{4}{\pi} \)
• C. \( \pi \)
• D. \( \frac{2}{\pi} \)

Hint:

The magnetic dipole moment depends on the area of the coil, and for identical wires, the circular coil produces a larger dipole moment than the square coil due to its larger area.

Answer 1

The Correct Option is B

Step 1: Understanding magnetic dipole moment.
The magnetic dipole moment \( M \) for a coil is given by the formula: \[ M = I A \] where \( I \) is the current and \( A \) is the area of the coil.
Step 2: Area comparison.
For a circular coil, the area \( A_{\text{circle}} = \pi r^2 \), and for a square coil, the area \( A_{\text{square}} = a^2 \), where \( r \) and \( a \) are the radii/side lengths of the circular and square coils, respectively. Since both coils are made from identical metal wires, they have the same total length, and their areas will be in proportion.
Step 3: Conclusion.
After calculating the ratio of the magnetic dipole moments, we find that the correct ratio is \( \frac{4}{\pi} \), which corresponds to option (B).