Magnetic Effects & Magnetism

JEE Main level, single correct, medium

249 of 276

Question 249 of 276

Two concentric circular loops of radii r1=30cm{r}_{1}=30cm and r2=50cm{r}_{2}=50cm are placed in X−YX-Y plane as shown in the figure. A current I=7AI=7A is flowing through them in the direction as shown in figure. The net magnetic moment of this system of two circular loops is approximately

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Answer: (B) −72k^Am2-\dfrac{7}{2}\hat{k}A{m}^{2}

Net magnetic moment of the system is
M⃗=−IA1k^+IA2k^\vec{M}=-I{A}_{1}\hat{k}+I{A}_{2}\hat{k} (Here currents in both circular loops are in opposite direction)
M⃗=−Iπ(0.5)2k^+Iπ(0.3)2k^\vec{M}=-I\pi {\left(0.5\right)}^{2}\hat{k}+I\pi {\left(0.3\right)}^{2}\hat{k}
M⃗=−7×227(25100−9100)k^\vec{M}=-7\times \dfrac{22}{7}\left(\dfrac{25}{100}-\dfrac{9}{100}\right)\hat{k}=−22(16100)k^=-22\left(\dfrac{16}{100}\right)\hat{k}
M⃗=−3.52k^Am2\vec{M}=-3.52\hat{k}A{m}^{2}
=−72k^Am2=-\dfrac{7}{2}\hat{k}A{m}^{2}

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