In the figure, the rectangular loop is pivoted about one side (of length .060 m)

Question

In the figure, the rectangular loop is pivoted about one side (of length .060 m) that coincides with the y-axis. The end (length .020 m) of the loop that lies in the x-z plane makes an angle of 37 degrees with the x-axis as in the sketch. The loop carries a current of I=44 A in the direction shown (In the side of the loop that is along the y-axis the current is in the +y direction ). If there is a uniform magnetic field of magnitude 5.6 T in the x-direction, find the magnitude of the torque that the magnetic field exerts on the loop

In the figure, the rectangular loop is pivoted about one side (of length .060 m) that coincides with the y - axis. The end (length .020 m) of the loop that lies in the x - z plane makes an angle of 37 degrees with the x - axis as in the sketch. The loop carries a current of I=44 A in the direction shown (In the side of the loop that is along the y - axis the current is in the +y direction ). If there is a uniform magnetic field of magnitude 5.6 T in the x - direction, find the magnitude of the torque that the magnetic field exerts on the loop

Explanation / Answer

F = il × B so the forces on the top and bottom segments cancel out, and the force on the vertical segment not on the y-axis will be exerted in the +z direction. For this segment, the angle between the current and the B-field is 90 degrees, so the force will just be ilB.

F = ilB = (44 A)(0.06 m)(5.6 T) = 14.784 N

The force is exerted at an angle of 53 degrees with respect to the z-axis along a moment arm of 0.02 m, for a torque of:

= rF sin = (0.02 m)(14.784 N)(0.798636) = 0.236 N-m

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