Question

$P$ and $Q$ are two concentric circular loop carrying current $i _{1}$ and $i _{2}$ as shown in figure. If ratio of their radii is $3: 2$ and ratio of the flux densities at the centre $O$ due to $P$ and $Q$ is $1: 3$ then the value of $\frac{ i _{1}}{ i _{2}}$ will be :-

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

Answer 1

Answer: (A)

$\frac{B_{1}}{B_{2}}=\frac{1}{3} $
$\left\{\right.$ Also, $\left.B=\frac{\mu_{0} i}{2 R}\right\}$
$\Rightarrow \frac{ i _{1} R_{2}}{ i _{2} R _{1}}=\frac{1}{3} $
$\Rightarrow \frac{ i _{1}}{ i _{2}}=\frac{1}{3} \times \frac{3}{2}=\frac{1}{2}$