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:

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U = - P → . B - F = - ∂ U ∂ r = P d B d r F = i 2 π a 2 × d d r μ 0 i 1 2 π r F = i 1 i 2 π 0 a 2 2 1 r 2 F ∝ a r 2 As r = d F ∝ a 2 d 2

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