The magnetic field intensity at the point O o | vedclass

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Question

(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 $B C$ wil

Vedclass · Accepted Answer

$\frac{\mu_0 i}{4 \pi}\left[\frac{3 \pi}{2 a}+\frac{\sqrt{2}}{b}\right]$

Vedclass · 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

$\bar{B}_1=2\left[\frac{\mu_0 i}{4 \pi b}\left(\sin 45^{\circ}+0ight)ight]=\frac{\mu_0 i}{2 \sqrt{2} \pi b} \otimes$

$\vec{B}$ due to circular part

$\bar{B}_2=\frac{\mu_0 i}{2 a}\left[\frac{\left(\frac{3 \pi}{2}ight)}{2 \pi}ight]=\frac{3 \mu_0 i}{8 a} \otimes$

$\overline{B_{	ext {net }}}=\overline{B_1}+\bar{B}_2=\mu_0 i\left[\frac{3}{8 a}+\frac{1}{2 \sqrt{2} \pi b}ight]=\frac{\mu_0 i}{4 \pi}\left[\frac{3 \pi}{2 a}+\frac{\sqrt{2}}{b}ight]$

The magnetic field intensity at the point $O$ of a loop with current $i$, whose shape is illustrated below is

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