Final answer:
The angle at which torque on a current loop is a certain percentage of the maximum can be found by solving for the angle at which sine of that angle equals the percentage in decimal form.
Step-by-step explanation:
The question relates to the calculation of torque on a current-carrying loop within a magnetic field. The torque exerted on a current loop can be calculated using the formula T = NIAB sin θ, where T is the torque, N is the number of turns, I is the current, A is the area of the loop, B is the magnetic field strength, and θ is the angle between the plane of the loop and the magnetic field direction.
• To find the angle at which the torque is a certain percentage of the maximum, we look at the sine function part of the equation. The maximum torque occurs when θ is 90 degrees (sin 90° = 1), meaning that the loop is perpendicular to the magnetic field. Therefore, for torque to be a percentage of the maximum, we must find the angle where sin θ equals that percentage.
• For example, to find at what angle the torque is 90% of maximum, you solve sin θ = 0.9, which gives an angle of θ approximately 64.2 degrees. Similarly, for 50% of maximum torque, solve sin θ = 0.5 to get θ as 30 degrees, and for 10% of maximum, solve sin θ = 0.1 to find θ approximately 5.7 degrees.