Question

$A$ and $B$ are two concentric circular conductors of centre $0$ and carrying currents $I_1$ and $I_2$ as shown in the figure. The ratio of their radii is $1:2$ and ratio of the flux densities at $0$ due to $A$ and $B$ is $1:3$.The value of $I_1/I_2$ will be

• A. 1/6
• B. 1/4
• C. 1/2
• D. 1/3

Answer 1

Answer: (A)

Magnetic field produced at the centre by loops,
$B_1=\frac{{\mu }_0{I}_1}{2r_1},sBl2=\frac{{\mu }_0{I}_2}{2r_2}$
$\frac{B_1}{B_2}=\frac{I_1}{I_2}\times \frac{r_2}{r_1}$
But given $\frac{B_1}{B_2}=\frac{1}{3}$
$\therefore \frac{1}{3}=\frac{I_1}{I_2}\times \frac{2}{1}$
$\therefore \frac{I_1}{I_2}=\frac{1}{6}$