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Question

Two infinitely long conductors carries current I, each along the x-axis and y-axis, respectively. A small circular coil of radius R, mass m and having N turns is also carrying current I in anticlockwise direction. The plane of the loop is parallel to the xy-plane, with its centre at a distance d along z-axis. Find the angular acceleration (in rad s2) of the loop.

Take: d=π2,I=10 A,N=1000,m=1 g



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Solution


The magnetic field due to the infinite wire at the centre of the loop is B=μoI2πd.

So, net magnetic field will be,

Bo=2μoI2πd=μoI2πd

Now, torque on the loop,

τ=MBsinθ=NIABsinθ

τ=NI(πR2)(μoI2πd)sin90

τ=μoNI2R22d=Iα

μoNI2R22d=(mR22)α

α=2μoNI2md=2×4π×107×1000×1020.001×π/2

α=80 rad/s2

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