Question

The magnitude of the magnetic field $(B)$ due to loop $ABCD$ at the origin $(O)$ is

• A. zero
• B. $\frac{\mu_{0}\left(b-a\right)}{24ab}$
• C. $\frac{\mu_{0}I}{4\pi}\left[\frac{b-a}{ab}\right]$
• D. $\frac{\mu_{0}I}{4\pi}\left[2\left(b-a\right)+\frac{\pi}{3}\left(a+b\right)\right]$

Answer 1

Answer: (B)

$\frac{\mu_{0}\left(b-a\right)}{24ab}$

Answer 2

Net magnetic field due to loop ABCD at O is $B = B_{AB} + B_{BC} + B_{CD} + B_{DA}$ $=0+\frac{\mu_{o}I}{4\pi a}\times\frac{\pi}{6}+0-\frac{\mu _{o}I}{4\pi b}\times \frac{\pi }{6}=\frac{\mu_{o}I}{24a}-\frac{\mu_{o}I}{24a}=\frac{\mu_{o}I}{24b}=\frac{\mu_{o}I}{24ab}\left(b-a\right)$