Q 12-04-024NEETJEE MainMedium
A current $I$ flows around a closed loop made of two radii of a circle of radius $R$ joined by the quarter-circle arc between them. The magnetic field at the centre of the circle is
Answer: (A) $\dfrac{\mu_0 I}{8R}$
The two straight parts point along radii, so their lines pass through the centre and give no field there.
An arc subtending angle $\theta$ gives $B = \dfrac{\mu_0 I}{4\pi R}\theta$. For a quarter circle, $\theta = \dfrac{\pi}{2}$:
$$B = \frac{\mu_0 I}{8R}$$
Solution by Sreeraj P, M.Sc Physics