Question

In the loop shown, the magnetic induction at the point $O$ is

• A. $\frac {\mu_0 I}{8}({\frac {R_1-R_2}{R_1R_2})}$
• B. $\frac {\mu_0 I}{8}({\frac {R_1+R_2}{R_1R_2})}$
• C. $\frac {\mu_0 I}{8}({\frac {R_1R_2}{R_1+R_2} )}$
• D. $Zero$

Answer 1

Answer: (B)

$\frac {\mu_0 I}{8}({\frac {R_1+R_2}{R_1R_2})}$

Answer 2

Net magnetic field at O
$B = B_{1}+B_{2} = \frac{-\pi/2}{2\pi}-\frac{\mu_{0}I}{2R_{1}}+\frac{\pi/2}{2\pi}\cdot\frac{\mu_{0}I}{2R_{2}}$
$= \frac{\mu_{0}I}{8}\left(\frac{R_{1}+R_{2}}{R_{1}R_{2}}\right)$