Question

Magnetic field at the centre $O$ due to the given structure is

• A. $\frac{\mu_{0} I}{4 R}\left[\frac{3}{2}+\frac{1}{\pi}\right] \odot$
• B. $\frac{\mu_{0} I}{2 R}\left[3+\frac{1}{\pi}\right] \otimes$
• C. $\frac{\mu_{0} I}{4 R}\left[\frac{3}{2}+\frac{1}{\pi}\right] \otimes$
• D. $\frac{\mu_{0}I}{4 R}\left[3+\frac{2}{\pi}\right] \odot$

Answer 1

Answer: (C)

$B=B_{\text {due to circular arc }}+B_{\text {due to staight wires }}$
$=\frac{\mu_{0} i}{2 R}\left(\frac{3 \pi}{2 \cdot(2 \pi)}\right)+\frac{\mu_{0} i}{4 \pi R}$
$\Rightarrow B=\frac{\mu_{0} i}{4 R}\left(\frac{3}{2}+\frac{1}{\pi}\right) \otimes$