2025 Moving Charges and MagnetismMagnetic Dipole Moment of Current Loop Easy Question 1 of 5 in Magnetic Dipole Moment of Current Loop

A $2\text{ amp}$ current is flowing through two different small circular copper coils having radii ratio $1:2$. The ratio of their respective magnetic moments will be:

A 1:4
B 1:2
C 2:1
D 4:1

The answer is A.

Solution

Magnetic moment is $M = NIA = I(\pi r^2) \propto r^2$. Thus $M_1/M_2 = (r_1/r_2)^2 = (1/2)^2 = 1/4$.

The magnetic dipole moment of a current loop is $M = N I A = N I (\pi r^2)$. Since the current $I$ and number of turns $N$ are identical, the magnetic moment is directly proportional to the square of the coil radius: $M \propto r^2$. Therefore, $\frac{M_1}{M_2} = \left(\frac{r_1}{r_2}\right)^2 = \left(\frac{1}{2}\right)^2 = \frac{1}{4}$.

Concept Magnetic Dipole Moment

Magnetic Dipole Moment of Current Loop in past papers

5 questions from this chapter have appeared across 5 exam years.