Question
The magnetic field intensity at the point $O$ of a loop with current $i$, whose shape is illustrated below is
✓
Answer
(a)
$\bar{B}$ due to square part :-
$\vec{B}$ due to side $O A$ and $O C$ will be zero at point $O$
$\bar{B}$ due to side $A B$ and $B C$ will be equal so
$\bar{B}_1=2\left[\frac{\mu_0 i}{4 \pi b}\left(\sin 45^{\circ}+0\right)\right]=\frac{\mu_0 i}{2 \sqrt{2} \pi b} \otimes$
$\vec{B}$ due to circular part
$\bar{B}_2=\frac{\mu_0 i}{2 a}\left[\frac{\left(\frac{3 \pi}{2}\right)}{2 \pi}\right]=\frac{3 \mu_0 i}{8 a} \otimes$
$\overline{B_{\text {net }}}=\overline{B_1}+\bar{B}_2=\mu_0 i\left[\frac{3}{8 a}+\frac{1}{2 \sqrt{2} \pi b}\right]=\frac{\mu_0 i}{4 \pi}\left[\frac{3 \pi}{2 a}+\frac{\sqrt{2}}{b}\right]$
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