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
JEE MAIN 2019, Diffcult
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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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