Final answer:
The magnetic force acting on the right section of the loop results in a torque that can be calculated via the right-hand rule and the equation t = rF sin θ. This force is perpendicular to the magnetic field and the current's direction, contributing to the total torque which is the sum of torques on both vertical segments of the loop.
Step-by-step explanation:
The components of the magnetic force acting on the right section of the loop can be determined considering that the loop is located in a uniform magnetic field and carries a current I. If the right vertical segment of the loop is considered, the force exerted on this segment due to the magnetic field can be found using the right-hand rule. The force will be perpendicular to both the magnetic field and the direction of the current, resulting in a torque about the shaft. According to the right-hand rule, if we curl the fingers of the right hand in the direction of the current and then into the direction of the magnetic field (which is assumed to be uniform across the loop), our thumb will point in the direction of the force. On the right vertical segment, this force acts inwards (or outwards) depending on the direction of the current and magnetic field. As such, this force, along with the force on the left vertical segment, creates a torque with a magnitude that can be given by t = rF sin θ, where r is the lever arm, F is the force, and θ is the angle between r and F. For a rectangular loop with width w and height l, the magnetic forces on the side segments produce equal and opposite torques, resulting in no net force on the loop but a total torque that can be defined as double the torque on one of the vertical segments. Assuming the width of the loop is w, and the magnetic force F acts on the segment, the torque on each vertical segment is (w/2) F sin θ, and hence the total torque is the sum of the torques on both vertical segments.