Final answer:
The greatest torque on a wire loop in an electric motor occurs when the angle between the loop's area vector and the magnetic field is 90° or 270°, as this configuration maximizes the sine function used in the torque equation, resulting in the maximum torque value.
Step-by-step explanation:
The torque exerted on a wire loop within an electric motor is dependent on the angle between the area vector of the loop and the magnetic field. Using the formula T = NIAB sin θ, where T is torque, N is the number of turns, I is the current, A is the loop area, B is the magnetic field, and θ is the angle between the area vector and the magnetic field, we can deduce that the torque is maximized when sin θ reaches its peak value of 1. This corresponds to angles where θ is 90° and 270°. At these angles, the area vector is perpendicular to the magnetic field, resulting in the greatest possible torque on the wire loop according to the right-hand rule.