A nonplanar rigid loop has two vertical sections, numbered 1 and 3, which are 20

Question

A nonplanar rigid loop has two vertical sections, numbered 1 and 3, which are 20 cm long. It also has two 90° arc sections, numbered 2 and 4. The curved sections have a radius of 8 cm, and the centers are on the z-axis. The loop carries a current of 15 A, as shown. A straight wire lies on the z-axis and carries a current of 25 A, as shown.

The vertical axis that passes through the center of mass of the loop has coordinates of x = y = 4.42 cm. Find the magnitude of the torque on the loop, about this vertical axis.

Explanation / Answer

force on circular wires = 0

force on each vertical wire = u0 x 25 x 15 x 0.2/( 2pi x 0.08) = 1.875 x 10-4 N

r( perpandicular) for each wire = 0.0442 m

torque due to forces = 2 x 0.0442 x 1.875 x 10-4 = 1.6575 x 10-5 Nm

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