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,
$B_{1}=\frac{\mu_{0} I_{1}}{2 r_{1}}, s \,\,B l 2=\frac{\mu_{0} I_{2}}{2 r_{2}}$
$\frac{B_{1}}{B_{2}}=\frac{I_{1}}{I_{2}} \times \frac{r_{2}}{r_{1}}$
But given $\frac{B_{1}}{B_{2}}=\frac{1}{3}$
$\therefore \frac{1}{3}=\frac{I_{1}}{I_{2}} \times \frac{2}{1}$
$\therefore \frac{I_{1}}{I_{2}}=\frac{1}{6}$