22.8 Torque on a Current Loop: Motors and Meters
3 min read•june 18, 2024
Electric harness the power of magnetism to convert electrical energy into mechanical work. By placing a current-carrying loop in a magnetic field, a is generated, causing rotation. This fundamental principle underlies the operation of countless devices we use daily.
The interaction between current and magnetic field in motors is governed by key equations like the law and torque formula. Understanding these relationships helps explain how motors achieve continuous rotation through clever design elements like and commutators.
Torque on a Current Loop: Motors and Meters
Conversion of energy in motors
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- Motors convert electrical energy into mechanical work through the interaction of magnetic fields and electric currents
- Current-carrying loop experiences a torque when placed in an external magnetic field causing rotation and conversion of electrical energy to rotational kinetic energy
- acts on current-carrying wires causing torque on the loop
- represents current, length vector of wire, and magnetic field
- Force is perpendicular to both current and magnetic field resulting in torque
- Torque direction depends on current direction and magnetic field orientation
- Right-hand rule determines torque direction (fingers point in current direction, magnetic field lines into palm, thumb points in torque direction)
- can also be used to determine the direction of motion in motors
Torque calculation for current loops
- Torque on a current-carrying loop in a uniform magnetic field:
- represents torque vector
- of loop, ( number of turns, current, loop area, unit vector normal to loop plane)
- external magnetic field
- Torque magnitude calculation:
- angle between magnetic dipole moment and magnetic field
- Maximum torque when loop perpendicular to magnetic field (), zero torque when loop parallel ( or )
- Work done by motor related to torque and angular displacement
- Work done: ( angular displacement)
- of the rotating loop contributes to the motor's inertia and affects its dynamic response
Function of brushes and commutators
- Brushes and commutators enable continuous rotation in DC motors
- is a split ring attached to and rotates with the (rotating part of motor)
- Made of insulated conductive segments (usually copper)
- Each segment connected to one end of armature windings
- Brushes are stationary contacts (carbon or graphite) pressing against the commutator
- Connected to external circuit supplying current to motor
- As armature rotates, commutator segments contact brushes, reversing current direction in armature windings
- Reversal ensures torque on armature always in the same direction for continuous rotation
- Without commutator and brushes, armature would oscillate instead of rotating continuously
- Brushes and commutator also transfer electrical power from stationary part (stator) to rotating armature
Electromagnetic Principles in Motors
- through the loop affects the motor's performance and efficiency
- plays a crucial role in the operation of motors, generating back EMF as the loop rotates in the magnetic field
- Changes in induce currents in the loop, following Faraday's law of induction
Key Terms to Review (24)
Angular momentum: Angular momentum is the rotational analog of linear momentum, representing the quantity of rotation of an object. It is a vector quantity given by the product of an object's moment of inertia and its angular velocity.
Angular Momentum: Angular momentum is a measure of the rotational motion of an object around a fixed axis. It describes the object's tendency to continue rotating and the amount of torque required to change its rotational state. This concept is fundamental in understanding the dynamics of rotating systems and is crucial in various areas of physics, from the motion of satellites to the behavior of subatomic particles.
Armature: The armature is a crucial component in the operation of electric motors, generators, and other electromechanical devices. It refers to the rotating part of the device that carries the current-carrying windings, which interact with the magnetic field to produce torque or voltage.
Brushes: Brushes are essential components in electric motors and generators, serving as the interface between the stationary and rotating parts of the device. They facilitate the transfer of electric current between the fixed and moving components, enabling the conversion of electrical energy to mechanical energy (in motors) or vice versa (in generators).
Commutator: A commutator is a device found in electric motors and generators that helps to convert the alternating current (AC) generated by the rotating armature into a direct current (DC) output. It plays a crucial role in the operation and efficiency of these electromechanical devices.
Current Loop: A current loop is a continuous path through which an electric current flows. It is a fundamental concept in electromagnetism, as the flow of electric current through a loop generates a magnetic field that can interact with other magnetic fields or be influenced by external magnetic fields.
DC Motor: A DC motor is an electromechanical device that converts direct current (DC) electrical energy into rotational mechanical energy. It is a fundamental component in many applications, including household appliances, industrial machinery, and transportation systems.
Electromagnetic Induction: Electromagnetic induction is the process by which a changing magnetic field induces an electromotive force (EMF) in a conductor, causing an electric current to flow. This phenomenon is the fundamental principle behind the operation of many electrical devices and systems, including transformers, generators, and motors.
Fleming's Left-Hand Rule: Fleming's left-hand rule is a mnemonic device used to determine the direction of the force experienced by a current-carrying conductor in a magnetic field. It provides a simple and intuitive way to visualize the relationship between the direction of the current, the magnetic field, and the resulting force.
Galvanometer: A galvanometer is an instrument for detecting and measuring small electric currents by deflection of a needle. It operates on the principle that an electric current passing through a coil produces a magnetic field.
Galvanometer: A galvanometer is a sensitive instrument used to detect and measure small electric currents. It operates on the principle of the torque experienced by a current-carrying loop in a magnetic field, and is a crucial component in the functioning of voltmeters and ammeters.
Lorentz force: The Lorentz force is the force experienced by a charged particle moving through an electric and magnetic field. It is given by the equation $\mathbf{F} = q(\mathbf{E} + \mathbf{v} \times \mathbf{B})$, where $q$ is the charge, $\mathbf{E}$ is the electric field, $\mathbf{v}$ is the velocity of the particle, and $\mathbf{B}$ is the magnetic field.
Lorentz Force: The Lorentz force is the force exerted on a moving charged particle when it is placed in a magnetic field. It is a fundamental concept in electromagnetism that describes the interaction between electric and magnetic fields and the motion of charged particles.
Magnetic Dipole Moment: The magnetic dipole moment is a vector quantity that describes the strength and orientation of a magnetic dipole, which is a pair of equal and opposite magnetic poles separated by a small distance. It is a fundamental property of certain particles and systems that exhibit a magnetic field.
Magnetic flux: Magnetic flux is the measure of the quantity of magnetism, taking into account the strength and extent of a magnetic field. It is calculated as the product of the magnetic field and the area through which it passes, perpendicular to the field.
Magnetic Flux: Magnetic flux is a measure of the total amount of magnetic field passing through a given surface or area. It represents the strength and distribution of a magnetic field and is a fundamental concept in the study of electromagnetism and its applications.
Meters: Meters are units of measurement used to quantify length, distance, and various other physical quantities. They are a fundamental unit in the International System of Units (SI) and are essential in the fields of physics, engineering, and many other scientific disciplines.
Motors: Motors are electromechanical devices that convert electrical energy into mechanical energy, enabling the generation of rotational or linear motion. They are fundamental components in a wide range of applications, from household appliances to industrial machinery, playing a crucial role in the conversion and control of power.
Newton-Meter: A newton-meter (N⋅m) is a unit of torque, which is a measure of the rotational force that causes an object to rotate about an axis, fulcrum, or pivot. This unit combines the units of force (newton) and distance (meter), representing the product of force and the perpendicular distance from the axis of rotation to the line of action of the force. The newton-meter is a fundamental unit in the study of rotational dynamics and equilibrium conditions.
Newton-meters: A newton-meter (N·m) is the unit of torque in the International System of Units (SI). It measures the amount of force applied over a distance, typically represented as the rotational equivalent of work.
SI unit of torque: The SI unit of torque is the newton-meter (Nm), which measures the rotational force applied to an object. Torque quantifies the tendency of a force to rotate an object about an axis.
Tesla: The tesla (T) is the SI unit of magnetic field strength or magnetic flux density. It measures how much force a magnetic field exerts on moving charges or current-carrying wires.
Tesla: The tesla (T) is the unit of magnetic flux density or magnetic induction in the International System of Units (SI). It is named after the Serbian-American inventor and electrical engineer Nikola Tesla, who made significant contributions to the design of the modern alternating-current (AC) electrical supply system.
Torque: Torque is the rotational equivalent of force, representing the ability to cause an object to rotate about a specific axis or pivot point. It is the product of the force applied and the perpendicular distance between the axis of rotation and the line of action of the force, and it plays a crucial role in the study of rotational motion and equilibrium.