13.1 Faraday’s Law
2 min read•june 24, 2024
and are key concepts in electromagnetism. They explain how changing magnetic fields create electric currents, powering everything from generators to transformers.
Understanding these principles is crucial for grasping how electricity and magnetism interact. We'll explore how magnetic flux is calculated and how Faraday's law describes the relationship between changing magnetic fields and induced electric currents.
Magnetic Flux and Faraday's Law
Magnetic flux calculation
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- Magnetic flux () quantifies the number of passing through a surface
- Influenced by magnetic field strength (), surface area (), and angle () between field lines and surface normal
- Formula:
- Maximum flux when field lines perpendicular to surface ():
- Zero flux when field lines parallel to surface ():
- SI unit: (Wb), where 1 Wb = 1 T·m²
- Examples: flux through a loop in a uniform magnetic field, flux through a coil in a changing magnetic field
- (B) represents the concentration of per unit area
Faraday's law for induced emf
- Faraday's law: () in a closed loop equals negative rate of change of magnetic flux () with time ()
- Induced emf () formula:
- Negative sign indicates induced emf opposes change in magnetic flux ()
- Factors inducing emf by changing magnetic flux:
- Varying magnetic field strength ()
- Altering loop area ()
- Changing loop orientation relative to magnetic field ()
- SI unit for induced emf: volt (V)
- Examples: emf induced in a coil by a changing current in a nearby coil (transformer), emf induced in a conductor moving through a magnetic field (generator)
- Induced emf () formula:
- The can be used to determine the direction of induced current in a loop
Induced emf from relative motion
- Relative motion between magnet and coil induces emf in coil by changing magnetic flux (Faraday's law)
- Moving magnet relative to stationary coil
- Magnet approaching or receding from coil changes flux, inducing emf
- Induced emf polarity depends on magnet's motion direction and pole orientation
- Moving coil relative to stationary magnet
- Coil moving through magnetic field changes flux, inducing emf
- Induced emf polarity depends on coil's motion direction and field orientation
- Moving magnet relative to stationary coil
- Induced emf magnitude depends on rate of change of magnetic flux, influenced by:
- Magnet strength
- Relative motion speed
- Number of coil turns
- Examples: emf induced in a coil by a moving bar magnet, emf induced in a conductor moving through a magnetic field (electric guitar pickup)
Electromagnetic Induction and Materials
- affects the strength of magnetic fields in different materials
- results from the interaction between moving charges and magnetic fields
Key Terms to Review (28)
Back emf: Back electromotive force (back emf) is the voltage generated by an electric motor or generator that opposes the applied voltage. It is a consequence of electromagnetic induction and acts to limit the current in the circuit.
Eddy Currents: Eddy currents are circular electric currents that are induced within a conductive material when it is exposed to a changing magnetic field. These currents flow in a direction that opposes the changes in the magnetic field, creating their own opposing magnetic field.
Electromagnetic Force: The electromagnetic force is one of the four fundamental forces in nature, along with the strong nuclear force, the weak nuclear force, and gravity. It is the force that arises between electrically charged particles, and it is responsible for a wide range of phenomena, from the attraction between opposite charges to the repulsion between like charges, as well as the behavior of electric and magnetic fields.
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 fundamental to the operation of many electrical devices and is crucial in understanding the relationship between electricity and magnetism.
Electromotive Force (EMF): Electromotive force, or EMF, is the voltage or potential difference generated by a source of electrical energy, such as a battery, generator, or other electrochemical device. It represents the maximum possible voltage that can be delivered by the source, and it drives the flow of electric current through a circuit.
Emf: Electromotive force (emf) is the voltage generated by a source such as a battery or by changing magnetic fields. It is the driving force that causes electrons to move in a circuit.
Faraday Disk: The Faraday disk, also known as the Faraday wheel, is a simple electrical generator that demonstrates the principles of electromagnetic induction. It consists of a metal disk or wheel that rotates between the poles of a magnet, generating an electric current in the process.
Faraday's law: Faraday's law states that a change in magnetic flux through a circuit induces an electromotive force (emf) in that circuit. This principle is crucial for understanding how magnetic fields interact with electric circuits and lays the foundation for many applications in electromagnetism.
Flux Density: Flux density is a measure of the amount of a physical quantity, such as a field or flow, passing through a given area. It is the ratio of the total flux to the area over which it is measured, and is a fundamental concept in fields like electromagnetism and fluid dynamics.
Flux linkage: Flux linkage is a measure of the total magnetic flux that passes through a coil of wire, multiplied by the number of turns in the coil. It represents how much magnetic field is linked with the coil and is crucial in understanding how changes in magnetic fields can induce electromotive force (EMF) in circuits. This concept plays a central role in understanding electromagnetic induction and its applications, highlighting how electricity can be generated from magnetic fields.
Heinrich Lenz: Heinrich Lenz was a Russian physicist who formulated the fundamental principle that describes the direction of the induced current in an electromagnetic induction system. This principle, known as Lenz's Law, is a crucial concept in understanding the behavior of electromagnetic phenomena and its applications in various areas of physics.
Induced Electromotive Force: Induced electromotive force (EMF) is the voltage or potential difference generated in a conductor when it experiences a changing magnetic field, as described by Faraday's law of electromagnetic induction. This induced voltage can drive an electric current in the conductor, powering various electrical devices and systems.
Lenz's Law: Lenz's law is a fundamental principle in electromagnetic induction that describes the direction of the induced current in a conductor. It states that the direction of the induced current will be such that it opposes the change in the magnetic field that caused it, in accordance with Faraday's law of electromagnetic induction.
Magnetic field lines: Magnetic field lines are imaginary lines that represent the direction and strength of a magnetic field. They emerge from the north pole of a magnet and enter the south pole, forming continuous loops.
Magnetic Field Lines: Magnetic field lines are the invisible lines that represent the direction and strength of a magnetic field. They are used to visualize and understand the behavior of magnetic fields, which are crucial in various topics related to electromagnetism and electromagnetic induction.
Magnetic flux: Magnetic flux quantifies the total magnetic field passing through a given area. It is measured in Weber (Wb) and mathematically given by $\Phi_B = B \cdot A \cdot \cos(\theta)$.
Magnetic Permeability: Magnetic permeability is a measure of the ability of a material to support the formation of a magnetic field within itself. It describes the degree of magnetization of a material in response to an applied magnetic field, and is a fundamental property that determines the strength and behavior of magnetic fields within a material.
Michael Faraday: Michael Faraday was a pioneering scientist known for his groundbreaking work in electromagnetism and electrochemistry during the 19th century. His contributions, particularly in discovering electromagnetic induction and formulating Faraday's Law, laid the foundation for modern electrical engineering and technology.
Motional EMF: Motional EMF, or electromotive force, is the voltage induced in a conductor when it moves through a magnetic field. This phenomenon is described by Faraday's Law of Electromagnetic Induction and plays a crucial role in the operation of various electrical devices and machines.
Right-hand rule: The right-hand rule is a mnemonic used to determine the direction of the magnetic field surrounding a current-carrying conductor. Point your thumb in the direction of the current and curl your fingers; your fingers indicate the direction of the magnetic field lines.
Right-Hand Rule: The right-hand rule is a mnemonic device used to determine the direction of various quantities related to electromagnetism, such as the direction of magnetic fields, the motion of charged particles in magnetic fields, and the direction of the magnetic force on a current-carrying conductor. It provides a simple and intuitive way to visualize and remember these directional relationships.
Solenoid: A solenoid is a coil of wire designed to create a uniform magnetic field in its interior when an electric current passes through it. It is commonly used in electromagnets, inductors, and valves.
Solenoid: A solenoid is a tightly wound coil of wire, often cylindrical in shape, that produces a magnetic field when an electric current passes through it. Solenoids are fundamental components in the study of electromagnetism and have applications in various areas of physics, including magnetic fields, magnetic force, and electromagnetic induction.
Tesla: The tesla (T) is the SI unit of magnetic flux density, representing the strength of a magnetic field. One tesla is defined as one weber per square meter.
Tesla: The tesla (T) is the unit of magnetic flux density, or magnetic field strength, in the International System of Units (SI). It is named after the Serbian-American inventor Nikola Tesla, who made significant contributions to the field of electromagnetism. The tesla is a fundamental unit that is essential in understanding and describing various electromagnetic phenomena and their applications.
Weber: The weber (Wb) is the SI unit of magnetic flux, representing the quantity of magnetism. One weber is equal to one tesla meter squared ($1 \, \text{Wb} = 1 \, \text{T} \cdot m^2$).
Weber: The weber (symbol: Wb) is the unit of magnetic flux in the International System of Units (SI). It is named after the German physicist Wilhelm Eduard Weber. The weber is a fundamental unit that is closely related to the concepts of magnetic field, electromagnetic induction, and the functioning of various electrical and electronic devices.
Φ_B: Φ_B, also known as the magnetic flux, is a fundamental concept in electromagnetism that represents the amount of magnetic field passing through a given surface or area. It is a crucial parameter in understanding Faraday's Law of Electromagnetic Induction, which describes the relationship between changing magnetic fields and the induced electromotive force (EMF) in a conductive loop or circuit.