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STD 12 - 4. Moving charges and magnetism — NEET STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceNEETSTD 12 - 4. Moving charges and magnetism4 Marks
MCQ
An infinitely long current carrying wire and a small current carrying loop are in the plane of the paper as shown. the radius of the loop is $a$ and distance of its centre from the wire is $d (d >> a)$. If the loop applies a force $F$ on the wire then
  • A
    $F = 0$
  • B
    $F \propto \left( {\frac{a}{d}} \right)$
  • C
    $F \propto \left( {\frac{a^2}{d^3}} \right)$
  • ✓
    $F \propto {\left( {\frac{a}{d}} \right)^2}$
✓

Answer

Correct option: D.
$F \propto {\left( {\frac{a}{d}} \right)^2}$
d
Force on one pole

$F = \frac{{m{\mu _0}I}}{{2\pi \sqrt {{d^2} + {x^2}} }}$

$m=$ pole strength

Total force $=2 F \sin \theta$

$=\frac{2 \times \mu_{0} \operatorname{Im} \times x}{2 \pi \sqrt{d^{2}+a^{2}} \sqrt{d^{2}+a^{2}}}=\frac{\mu_{0} \operatorname{Im} x}{\pi\left[d^{2}+a^{2}\right]}$

$=m 2 x=M=I \pi a^{2}$

Total force $=\frac{\mu_{0} I a^{2}}{2\left(d^{2}+a^{2}\right)}$

$\approx \frac{\mu_{0} I a^{2}}{2 d^{2}} \quad[\because d>>a]$

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