Final answer:
The torque on a current loop in a magnetic field varies with the sine of the angle between the field and the loop's normal. The angles at which the torque is 90%, 50%, and 10% of its maximum are approximately 64.16°, 30°, and 5.74°, respectively.
Step-by-step explanation:
The torque on a current loop in a magnetic field depends on the angle between the magnetic field and the normal to the plane of the loop. The torque (τ) on the loop is given by the equation τ = NIAB × sine of the angle (θ), where N is the number of turns, I is the current, A is the area of the loop, and B is the magnetic field strength.
To find the angles at which the torque is a certain percentage of maximum, we look at the sine function, which has its maximum value of 1 when the angle is 90°. Thus, maximum torque occurs at 90°. To find angles corresponding to (a) 90.0%, (b) 50.0%, and (c) 10.0% of the maximum torque, we solve for the angle when sine(θ) is 0.9, 0.5, and 0.1, respectively.
- (a) sine(θ) = 0.9, the angle θ is approximately 64.16°
- (b) sine(θ) = 0.5, the angle θ is 30°
- (c) sine(θ) = 0.1, the angle θ is approximately 5.74°
Note that for angles not exactly corresponding to known sine values, inverse sine (arcsine) can be used to find the angle.