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Q.

Two long parallel wires in the YZ plane at a distance 2a apart carry a steady current I in opposite directions. Midway between the wires is a rectangular loop of wire of dimensions 2b×d carrying current I as shown in figure (b<a<2b). The loop is free to rotate about the z axis and the currents remain fixed to ‘I’ irrespective of the relative motion between the loop and the wire.
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Take a=8cm, b=6cm and d=5cm also let I=1A
Torque tending to rotate the rectangular loop about its axis when the angle between plane of loop and y axis ϕ=90°  (i.e., loop is in ZX plane) is 2.4×x×107Ncm. Find x
 

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Detailed Solution

In the figure Z-axis is into plane and  ϕ=90°
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F'=μ0I2d2πa2+b2,  So  F=μ0I2d2πa2+b2×aa2+b2×2

τ=F×2b=2μ0I2abdπ(a2+b2)=19.20×107N×cm



 
 

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