Sankalp NEET Full Test-3 Question-12 Solution

Question: 12. A 2 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

(1) 1: 4

(2) 1: 2

(3) 2: 1

(4) 4: 1

Answer: Option (1)

Explanation:

For a current loop the magnetic moment is proportional to the current and the area of the loop. The magnetic moment is given by \mu=NI A. For single-turn small circular coils we take N=1, so \mu=I A. The area of a circular coil is A=\pi r^2. Since the same current flows through both coils, the ratio of their magnetic moments equals the ratio of their areas:

\displaystyle \frac{\mu_1}{\mu_2}=\frac{I\pi r_1^2}{I\pi r_2^2}=\left(\frac{r_1}{r_2}\right)^2

Given the radii ratio r_1:r_2=1:2,

\displaystyle \frac{\mu_1}{\mu_2}=\left(\frac{1}{2}\right)^2=\frac{1}{4}

Thus the ratio of their magnetic moments is 1:4,

so Option (1) is correct.