Question

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

• A. $Zero$
• B. $\frac{{\mu }_{0}i(b-a)}{24ab}$
• C. $\frac{{\mu }_{0}i}{4\pi }\left[\frac{b-a}{ab}\right]$
• D. $\frac{{\mu }_{0}i}{4\pi }\left[a\right(b-a)+\frac{\pi }{3}(a+b\left)\right]$

Answer 1

The correct option is B $\frac{{\mu }_{0}i(b-a)}{24ab}$

Net magnetic field due to loop ABCD at ‘0’ is

$B_{net}=B_{AB}+B_{BC}+B_{DA}=0+\frac{{\mu }_{0}i}{4\pi a}\times \frac{\pi }{6}+0-\frac{{\mu }_{0}i}{4\pi b}\times \frac{\pi }{6}=\frac{{\mu }_{0}i}{24a}-\frac{{\mu }_{0}i}{24b}=\frac{{\mu }_{0}i}{24}\frac{(b-a)}{ab}$