A 2 A current is flowing through two different small circular copper coils having radii in the ratio 1 : 2. The ratio of their re…

Question

A 2 A current is flowing through two different small circular copper coils having radii in the ratio 1 : 2. The ratio of their respective magnetic moments will be:

1. A. 1 : 4 (Correct answer)
2. B. 1 : 2
3. C. 2 : 1
4. D. 4 : 1

Correct Answer

Option A — 1 : 4

Detailed Solution & Explanation

The correct answer is 1 : 4.

Key Points

• Magnetic moment of a current-carrying circular loop: $M=IA=I\pi r^2$.
• With the same current, $M\propto r^2$.
• $\dfrac{M_1}{M_2}=\dfrac{r_1^2}{r_2^2}=\left(\dfrac{1}{2}\right)^2=\dfrac{1}{4}$.