A circular coil of wire 8.40cm in diameter has 18.0 turns and carries a current

Question

A circular coil of wire 8.40cm in diameter has 18.0 turns and carries a current of 2.70 A. The coil is in a region where the magnetic field is 0.620T. What orientation of the coil gives the maximum torque on the coil? Please, enter the value of the angle between the field and the normal to the plane of What is this maximum torque in part (A) ? For what orientation of the coil is the magnitude of the torque 71.0% of the maximum found (B)? Please, enter the value of the angle between the field and the normal to the plane of

Explanation / Answer

Solving Torque problems:- There is obviously no torque (about the hinge) on the side which is hinged because there is no lever arm. The torques on the adjacent side obviously cancel because the current flows opposite directions. So only the far side matters. The magnetic torque is given by: N = r x F where F = c IL x B (I'm using c for # of coils, I for current, L for length of a side, B for the magnetic field) So N = r x (cIL x B) r has the same magnitude as L. The L vector is always perpendicular to B, so. N(magnetic) = cIL^2B cos theta where r is the distance from the hinge. The cosine comes about because you have max torque when the coil is vertical and the magnetic force is in the direction of rotation. You have no torque when the coil is horizontal and the magnetic force is toward the axis. The gravitational torque is given by: (weight/4 * 0 (hinge side) + weight/4 * L (opposite side) + 2 * weight/4 * L/2 (adjacent sides)) * sin (theta) = weight * L / 2 * sin (theta) I just added up the weight of each side times the distance from the CM to the axis. The sin comes about because there's no torque when the loop hangs straight down (gravity pulls directly away from axis) and maximum torque when it's horizontal and gravity pulls it down. Set the torques equal: cIL^2B cos theta = weight * L / 2 * sin (theta) theta = arctan (2 cILB / mg) They give you the current (I), the length of a side (L), the magnetic field (B), the mass. You know g. c (number of coils) is the square's perimeter divided by the entire length of wire. Plugnchug. Then plug that back in to get the magnetic and gravitational torques, which should be equal.

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