Q96 / 125 · BITSAT 2018 · Physics

A current $i$ flows through a loop as shown in figure. The magnetic field at the Centre $O$ is

Solution

The angle, subtended by arc $D E$ at $O$ is $\frac{π}{2}$ and $F C$ at $O = \frac{3 π}{2}$ the effective magnetic field at $O$ is

$B = B_{D E} + B_{F C}$

$= \frac{μ_{0} i}{4 π (3 r)} \times \frac{π}{2} + \frac{μ_{0} i}{4 π (r)} \times (\frac{3 π}{2})$

$= \frac{μ_{o} i}{8 r} [\frac{1}{3} + 3]$

$= \frac{5 μ_{o} i}{12 r}$ acting downwards

Hence, the correct answer is option: 'D'.