A rectangular loop of wire with length L = 29.5 cm and width W = 16.7 cm carries

Question

A rectangular loop of wire with length L = 29.5 cm and width W = 16.7 cm carries a current I1 = 1.92 A. A very long straight wire in the plane of the loop carries a current I2 = 11.5 A. The near edge of the loop is parallel to the long wire, and separated from it by a distance d = 11.9 cm.

1)What is the magnitude of the net force on the loop due to the current in the straight wire?

2)What is the magnitude of the net torque on the loop about its center point due to the current in the straight wire?

Explanation / Answer

Please kindly change values The long straight wire produces a magnetic field of B = u0 I1 / (2 pi r) = 2*10^-7 * 3.5 / r the force on each parallel side of the loop is F = I2 L B the closer side of the loop is at a distance r = h this gives a force of F1 = 1.5 * 0.45 * 2*10^-7 * 3.5 / 0.146 = 3.236 * 10^-6 N the farther side of the loop is at a distance r = h + w this gives a force of F2 = 1.5 * 0.45 * 2*10^-7 * 3.5 / 0.346 = 1.366 * 10^-6 N These are in opposite directions, so subtract. The forces on the sides of the loop perpendicular to the long wire are also in opposite directions, so they cancel each other completely. Result: 1.871 * 10^-6 N towards the straight wire

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