# A wire loop PQRSP is constructed by joining two semi - circular coils of radii $'r_1'\: and \: 'r_2'$ respectively as shown in the figure. If the current flowing in the loop is $'i'$ , then the magnetic induction at the point $'O'$ is :

$\begin {array} {1 1} (1)\;\large\frac{\mu_0i}{4} \bigg[ \large\frac{1}{r_1}-\large\frac{1}{r_2} \bigg] & \quad (2)\;\large\frac{\mu_0i}{4} \bigg[ \large\frac{1}{r_1}+\large\frac{1}{r_2} \bigg] \\ (3)\;\large\frac{\mu_0i}{2} \bigg[ \large\frac{1}{r_1}-\large\frac{1}{r_2} \bigg] & \quad (4)\;\large\frac{\mu_0i}{2} \bigg[ \large\frac{1}{r_1}+\large\frac{1}{r_2} \bigg] \end {array}$

Ans : (1)
$\large\frac{\mu_0i}{4} \bigg[ \large\frac{1}{r_1}-\large\frac{1}{r_2} \bigg]$