Question

Current is flowing in conducting wire shaped as shown in the figure. The radius of the curved part is $R$ and the length of straight portion is very large. The value of the magnetic field at the centre $O$ is $B=\frac{{\left(\mu \right)}_{0}I}{\pi R}\left(k\pi +\frac{1}{4}\right)$ , where the value of $k$ is

• A. $\frac{3}{2}$
• B. $\frac{3}{8}$
• C. $\frac{9}{2}$
• D. $\frac{9}{8}$

Answer 1

Answer: (B)

$B_A=0$
$B_B=\frac{{\mu }_0(2\pi -\pi /2)I}{4\pi }$
$B_C=\frac{{\mu }_{0}I}{4\pi R}$

$\therefore B_0=B_A+B_B+B_C=\frac{{\left(\mu \right)}_{o}I}{4\pi R}\left(\frac{3\pi }{2}+1\right)$
$B=\frac{{\left(\mu \right)}_{o}I}{\pi R}\left(\frac{3}{8}\pi +\frac{1}{4}\right)$
$B=\frac{{\left(\mu \right)}_{o}I}{\pi R}\left(\kappa \pi +\frac{1}{4}\right)$
When $\kappa =\frac{3}{8}$