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 $\kappa=\frac{3}{8}$