Question

A current $I$ is flowing through the loop, as shown in the figure. The magnetic field at centre $O$ is

• A. $\frac{7 \mu _{0} I}{16 \, R}\bigotimes$
• B. $\frac{7 \mu _{0} I}{16 \, R}\odot$
• C. $\frac{5 \mu _{0} I}{16 \, R}\bigotimes$
• D. $\frac{5 \mu _{0} I}{16 \, R}\odot$

Answer 1

Answer: (A)

$B=B_{1}+B_{2}$
$=\frac{\mu_0 I}{2 r_1}\left(\frac{3 \pi / 2}{2 \pi}\right)+\frac{\mu_0 I}{2 r_2}\left(\frac{\pi / 2}{2 \pi}\right)$
$=\frac{3}{8} \frac{\mu_0 I}{R}+\frac{\mu_0 I}{2(2 R)} \times \frac{1}{4}$
$=\frac{7}{16} \, \frac{\mu _{0} I}{R}\bigotimes$