Question

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

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

Answer 1

Answer: (C)

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