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 dda . If the loop applies a force F on the wire, then

Question

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 dd>>a . If the loop applies a force F on the wire, then

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For motion of the loop along  $$x-direction$$, P.E. is $$U(x)=$$−m→⋅B→As both m→ (of$$ $$loop) and B→(of$$ wire at $$loop) point normally into the plane of paper,$$U(x)=$$−$$mB=$$−π$$a2i$$⋅μ$$0I2$$$$π$$$$x=$$−μ$$0iIa22xP$$.E. decrease as loop moves closer to the wire. Force on the loop is attractive.$$F=dUdx=$$−μ$$0iIa221x2$$ At x $$=d$$,$$F=$$μ$$0iI2a22d2($$ Attraction $$)$$ ⇒F∝$$a2d2$$

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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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 dd>>a . If the loop applies a force F on the wire, then

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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