Magnetic Effects & Magnetism

JEE Main level, single correct, medium

227 of 276

Question 227 of 276

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 aa and distance of its centre from the wire is d(d≫a).d\left(d≫a\right). If the loop applies a force FF on the wire then:

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Answer: (A) F∝(ad)2F\propto {\left(\dfrac{a}{d}\right)}^{2}

U=−P⃗.B−U=-\vec{P}.B^{-}

F=−∂U∂r=PdBdrF=-\dfrac{\partial U}{\partial r}=P\dfrac{dB}{dr}

F=i2(πa2)×ddr(μ0i12πr)F={i}_{2}\left(\pi {a}^{2}\right)\times \dfrac{d}{dr}\left(\dfrac{{\mu }_{0}{i}_{1}}{2\pi r}\right)

F=i1i2π0a221r2F=\dfrac{{i}_{1}{i}_{2}{\pi }_{0}{a}^{2}}{2}\dfrac{1}{{r}^{2}}

F∝(ar)2F\propto {\left(\dfrac{a}{r}\right)}^{2}

As r=dr=d

F∝a2d2F\propto \dfrac{{a}^{2}}{{d}^{2}}

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