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4. Moving charges and magnetism — Physics STD 12 Science — Question

CBSE BoardEnglish MediumSTD 12 SciencePhysics4. Moving charges and magnetism1 Mark
MCQ
The magnetic field intensity at the point $O$ of a loop with current $i$, whose shape is illustrated below is
  • ✓
    $\frac{\mu_0 i}{4 \pi}\left[\frac{3 \pi}{2 a}+\frac{\sqrt{2}}{b}\right]$
  • B
    $\frac{\mu_0 i}{4 \pi^2}\left[\frac{2}{a}+b\right]$
  • C
    $\frac{\mu_0 i}{2 \pi}\left[\frac{1}{a}+\frac{1}{b}\right]$
  • D
    $\frac{\mu_0 i}{4 \pi}\left[\frac{1}{a}+\frac{1}{b}\right]$
✓

Answer

Correct option: A.
$\frac{\mu_0 i}{4 \pi}\left[\frac{3 \pi}{2 a}+\frac{\sqrt{2}}{b}\right]$
a
(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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