Question

A and B are concentric circular conductors with center O and carrying currents $I_1$ and $I_2$ as shown in fig. The ratio of their radii is 1: 2 and ratio of their flux densities at O is 1:3 The value of $\frac{I_1}{I_2}$ is

• A. $\frac{1}{6}$
• B. $\frac{1}{4}$
• C. $\frac{1}{2}$
• D. $\frac{1}{3}$

Answer 1

The correct option is A $\frac{1}{6}$


Given $R_1:R_2=1:2$
Magnetic flux density $\propto$ Field strength.
So, $B_1:B_2=1:3$

Magnetic field due to a current carrying loop at its centre
$B=\frac{n{\mu }_{0}i}{2r}$.
We can assume the number of turns $n=1$, since there is no data given.

$\frac{B_1}{B_2}=\frac{\frac{{\mu }_0{I}_1}{2R_1}}{\frac{{\mu }_0{I}_2}{2R_2}}=\frac{R_2}{R_1}\times \frac{I_1}{I_2}$
$\Rightarrow \frac{1}{3}=\frac{2}{1}\times \frac{I_1}{I_2}$
$\therefore \frac{I_1}{I_2}=\frac{1}{6}$