28.9:
Force On A Current Loop In A Magnetic Field
An electrical device transforming electrical energy into mechanical energy is known as a DC motor. It consists of a stationary part, the stator, and a rotating part, the rotor.
In motors, each wire loop is in a magnetic field; when current flows through the loop, the forces on the wire closest to the magnetic poles are directed in opposite directions, as determined by the right-hand rule. The magnetic field applies torque, which causes the shaft to rotate.
Consider a rectangular current-carrying loop of wire with sides of lengths a and b in a uniform magnetic field.
Recalling the magnetic force on a straight current-carrying wire equation, the magnetic force on side 1 and side 3 can be calculated, and the direction can be determined using the right-hand rule.
Similarly, the current on sides 2 and 4 are perpendicular to the magnetic field, and thus, the forces on these sides can be determined.
Finally, the net force on the loop can be calculated by adding all the forces on each side of the loop.
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:
Suggested Reading
- OpenStax. (2019). University Physics Vol. 2. [Web version], Pg 396 – 398. Retrieved from https://openstax.org/books/university-physics-volume-2@8ede2ba/pages/11-4-magnetic-force-on-a-current-carrying-conductor