Question

A current $I$ flows through a closed loop as shown in figure. The magnetic field induction at the centre $O$ is

• A. $\frac{{\mu }_{0}I}{4\pi R}\theta$
• B. $\frac{{\mu }_{0}I}{4\pi R}(\theta +\sin \theta )$
• C. $\frac{{\mu }_{0}I}{4\pi R}(\pi -\theta +\sin \theta )$
• D. $\frac{{\mu }_{0}I}{2\pi R}(\pi -\theta +\tan \theta )$

Answer 1

Answer: (D)

$B_O=B_{PQS}+B_{SP}$
$=\frac{{\mu }_0}{4\pi }\frac{I}{R}(2\pi -2\theta )+\frac{{\mu }_0}{4\pi }\frac{I}{R\cos \theta }(\sin \theta +\sin \theta )$
$=\frac{{\mu }_0}{2\pi }\frac{I}{R}[\pi -\theta +\tan \theta ]$