28.9 : Force On A Current Loop In A Magnetic Field

Magnetic forces on wires carrying current are most frequently applied in motors. A DC motor is a device that converts electrical energy into mechanical work. In motors, wire loops are enclosed in a magnetic field. When current flows through the loops, the magnetic field applies torque, which causes the shaft to rotate. The direction of the current is reversed once the loop's surface area is lined up with the magnetic field, causing a constant torque on the loop. During the process, commutators and brushes are used to reverse the current. The commutator is set to reverse the current flow at certain points to keep continual motion in the motor. A basic commutator has three contact areas to avoid and dead spots where the loop would have zero instantaneous torque at that point. The brushes press against the commutator, creating electrical contact between parts of the commutator during the spinning motion.

Consider a rectangular-shaped current-carrying loop of wire with sides of lengths a and b, such as a loop in a motor, placed in a uniform magnetic field, as shown in figure 1.

The loop of wire experiences forces that can be calculated by applying the equation for the magnetic force on a straight current-carrying wire to each of the sides. The force on side 1 and side 2 can be calculated as follows:

The magnitude of the current on side 3 and side 4 is the same but flows in the opposite direction to that on side 1 and side 2, respectively. Thus, the force on side 3 and side 4 is equal to the force on side 1 and side 2, respectively, with a negative sign. Finally, the total force in the current-carrying loop of wire is equal to the sum of the individual forces acting on each side of the loop and can be calculated as follows: