A rectangular coil consists of N 150 closely wrapped turns

A rectangular coil consists of N = 150 closely wrapped turns and has dimensions a = 0.400 m and b = 0.300 m. The coil is hinged along the y axis, and its plane makes an angle ? = 30.0° with the x axis (figure).

(a) What is the magnitude of the torque exerted on the coil by a uniform magnetic field B = 0.880 T directed in the positive x direction when the current is I = 1.20 A in the direction shown?

(b) If you are looking downward from the positive y direction, what is the expected direction of rotation of the coil?

Solution

Torque = r * F = b F cos theta

= b cos theta * (N I a B) = N I a b B cos theta

= 150 * 1.20 * 0.400 * 0.300 * 0.880 * cos 30

Torque = 16.46 N.m

All the torque comes from the force on the outer leg, giving a force in the k direction.

So we expect the angle theta to increase.