Question

The given diagram shows $A$ and $B$ which are two concentric circular conductors having the common centre $O$ . These conductors carry currents $i_1$ and $i_2$ , respectively and ratio of their radii is $1:2$ . If the ratio of the flux densities at $O$ due to $A$ and $B$ is $1:3$ , then calculate the value of the ratio of their respective currents, i.e., $\frac{i_1}{i_2}$ .

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

Answer 1

Answer: (D)

Magnetic field at the centre of circular coil is given by
$B=\frac{{\mu }_{0}I}{2r}$
$B\propto \frac{I}{r}$
$\Rightarrow B_A\propto \frac{I_1}{r_1}$
$\Rightarrow B_B\propto \frac{I_2}{r_2}$
$\Rightarrow \frac{B_A}{B_B}=\frac{I_1}{I_2}\times \frac{2r}{r}$
$\Rightarrow \frac{1}{3}=\frac{I_1}{I_2}\times 2$
$\Rightarrow \frac{I_1}{I_2}=\frac{1}{6}$