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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
A square loop $ABCD$, carrying a current $i,$ is placed near and coplanar with a long straight conductor $XY$ carrying a current $I,$ the net force on the loop will be
  • ✓
    $\frac{{2{\mu _0}Ii}}{{3\pi }}$
  • B
    $\frac{{{\mu _0}Ii}}{{2\pi }}$
  • C
    $\frac{{2{\mu _0}Ii{\rm{l}}}}{{3\pi }}$
  • D
    $\frac{{{\mu _0}Ii{\rm{l}}}}{{2\pi }}$
✓

Answer

Correct option: A.
$\frac{{2{\mu _0}Ii}}{{3\pi }}$
a
Force on arm $AB$ due to current in conductor $- XY$ is

$F_{1}=\frac{\mu_{0}}{4 \pi} \frac{2 l i L}{(L / 2)}=\frac{\mu_{0} I i}{\pi}$

acting towards $-17$ in the plane of loop.

Force on arm $CD$ due to current in conductor $XY$ is

$F_{2}=\frac{\mu_{0}}{4 \pi} \frac{2 I i L}{3(L / 2)}=\frac{\mu_{0} I i}{3 \pi}$

acting away from $-ill$ in the plane of loop.

$\therefore$ Net force on the loop $=F_{1}-F_{2}$

$=\frac{\mu_{0} I i}{\pi}\left[1-\frac{1}{3}\right]=\frac{2}{3} \frac{\mu_{0} I i}{\pi}$

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