23.2 Faraday’s Law of Induction: Lenz’s Law
3 min read•june 18, 2024
of Induction and are crucial concepts in electromagnetism. They explain how changing magnetic fields create electric currents and vice versa, forming the basis for many modern technologies.
These principles underpin the workings of transformers, generators, and induction cooktops. Understanding them is key to grasping how we harness electromagnetic energy in everyday life and advanced applications like machines.
Faraday's Law of Induction and Lenz's Law
Calculation of induced emf
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- Faraday's Law quantifies the relationship between changing and () in a loop of wire
- Expressed as , where is induced emf, is , and is time
- Negative sign indicates induced emf opposes the change in magnetic flux (Lenz's Law)
- Magnetic flux depends on , loop area , and angle between field and loop normal
- Formula:
- Units: webers (Wb) or -square meters (T·m²)
- Induced current in the loop related to induced emf and loop resistance by
- Larger emf or smaller resistance results in larger induced current (transformers, generators)
Direction prediction with Lenz's Law
- Lenz's Law states induced current flows in a direction that opposes the change in magnetic flux causing it
- Increasing magnetic flux induces current that creates a magnetic field opposing the increase (solenoids, electromagnets)
- Decreasing magnetic flux induces current that creates a magnetic field opposing the decrease (induction cooktops, braking systems)
- determines the direction of induced current
- Point thumb in the direction of the magnetic field
- Curl fingers in the direction of the current
- Palm faces the direction of the induced magnetic field
- Enables prediction of induced current direction without calculation (motors, generators)
- Lenz's Law is a consequence of the principle
Applications of electromagnetic induction
- Transformers use induction to change AC voltage
- Primary coil connected to AC source creates changing magnetic flux
- Secondary coil with different turns experiences induced emf, stepping voltage up or down (power grids, electronic devices)
- Generators convert mechanical energy to electrical energy
- Coil rotates in a magnetic field, inducing emf and current (power plants, wind turbines)
- Mechanical input can be from various sources (steam, water, wind)
- Induction cooktops heat cookware directly using high-frequency alternating current
- Coil beneath cooktop creates rapidly changing magnetic field
- Induced in cookware cause heating due to resistance (efficient, safe)
- uses induction for detailed body imaging
- Strong magnetic field aligns protons in body tissues
- Radio waves excite protons, causing precession and signal emission
- Induction coils detect signals, enabling image reconstruction (medical diagnosis, research)
Electromagnetic Theory and Induction
- describe the fundamental relationships between electric and magnetic fields, including Faraday's Law
- The explains the interaction between charged particles and electromagnetic fields, contributing to the understanding of induced currents
- characterizes the torque experienced by a current loop in a magnetic field, relevant in the study of magnetic materials and their behavior under induction
Key Terms to Review (39)
(peak) emf: Peak electromotive force (emf) is the maximum voltage generated in an AC generator during one cycle. It occurs when the rate of change of magnetic flux through the coil is at its highest.
$ ext{Phi}_B$: $ ext{Phi}_B$ is a fundamental quantity in Faraday's Law of Induction and Lenz's Law, representing the magnetic flux through a surface or loop. It is a measure of the magnetic field passing through a specific area and is a crucial concept in understanding electromagnetic induction and the generation of induced currents.
$arepsilon$: $arepsilon$ is a Greek letter that represents a small quantity or change in a physical quantity. In the context of physics, it is often used to denote an induced electromotive force (emf) or voltage that opposes the change in the magnetic field, as described by Faraday's law of induction and Lenz's law. It is also associated with the concept of back emf in electric motors and the inductance of a circuit.
Absolute pressure: Absolute pressure is the total pressure exerted on a system, including atmospheric pressure. It is measured relative to a perfect vacuum.
B: B is a fundamental quantity in the study of electromagnetism that represents the strength and direction of the magnetic field at a given point in space. It is a vector field that describes the magnetic force experienced by a moving charged particle or a current-carrying conductor.
Conservation of Energy: Conservation of energy is a fundamental principle in physics that states the total energy of an isolated system remains constant, it is said to be conserved over time. Energy can neither be created nor destroyed; rather, it can only be transformed or transferred from one form to another.
Eddy Currents: Eddy currents are electric currents that are induced within a conductive material when it is exposed to a changing magnetic field. These circulating currents create their own magnetic fields that oppose the original changing magnetic field, leading to various effects that are important in various applications.
Electromagnet: An electromagnet is a type of magnet in which the magnetic field is produced by the flow of electric current. Unlike permanent magnets, the magnetic field of an electromagnet can be easily turned on and off, making it a versatile and controllable source of magnetic fields.
Electromagnetic induction: Electromagnetic induction is the process by which a changing magnetic field within a closed loop of wire induces an electromotive force (emf) in the wire. It is a fundamental principle underlying many electrical technologies, such as transformers and electric generators.
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.
EMF: EMF, or electromotive force, is a fundamental concept in electricity and magnetism that represents the potential difference or voltage generated by a source of electrical energy, such as a battery or a generator. It is the driving force that causes electric charges to move through a circuit, and it is a crucial factor in understanding various electrical phenomena, including terminal voltage, Faraday's law of induction, eddy currents, and inductance.
Faraday's Law: Faraday's law describes the relationship between a changing magnetic field and the electric field it induces. It states that the magnitude of the induced electromotive force (emf) in a circuit is proportional to the rate of change of the magnetic flux through the circuit.
Faraday’s law of induction: Faraday's Law of Induction states that a change in magnetic flux through a loop induces an electromotive force (EMF) in the wire. The induced EMF is directly proportional to the rate of change of magnetic flux.
Generator: A generator is a device that converts mechanical energy into electrical energy through the process of electromagnetic induction. It is a crucial component in the generation and distribution of electrical power, enabling the transformation of various forms of energy into usable electricity.
Induced Electromotive Force: Induced electromotive force (EMF) refers to the voltage or potential difference generated in a conductor when it experiences a change in the magnetic field surrounding it. This phenomenon is the underlying principle behind Faraday's Law of Induction and Lenz's Law, which describe the relationship between changing magnetic fields and the induced electric currents they can generate.
Law of conservation of energy: The law of conservation of energy states that energy cannot be created or destroyed, only transformed from one form to another. The total energy in an isolated system remains constant over time.
Lenz’s law: Lenz's Law states that the direction of an induced current in a conductor by a changing magnetic field will be such that it creates a magnetic field opposing the change. This is a consequence of the conservation of energy.
Lenz's Law: Lenz's law is a fundamental principle in electromagnetism that describes the direction of the induced current or electromotive force (emf) generated by electromagnetic induction. It states that the direction of the induced current is always such that it opposes the change in the magnetic field that caused it, in accordance with Faraday's law of induction.
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 Field Strength: Magnetic field strength is a measure of the force exerted by a magnetic field on a moving electric charge or a magnetic dipole. It is a vector quantity that describes the magnitude and direction of the magnetic field at a specific location. This term is crucial in understanding the behavior of charged particles in a magnetic field, the principles of electromagnetic induction, and the effects of eddy currents on magnetic systems.
Magnetic field strength (magnitude) produced by a long straight current-carrying wire: Magnetic field strength (magnitude) produced by a long straight current-carrying wire is the intensity of the magnetic field that surrounds the wire due to the flow of electric current through it. It can be calculated using Ampere's Law and is directly proportional to the current and inversely proportional to the distance from the wire.
Magnetic field strength inside a solenoid: Magnetic field strength inside a solenoid is the intensity of the magnetic field created within a coil of wire when an electric current passes through it. It is uniform and parallel to the axis of the solenoid.
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.
Magnetic Resonance Imaging: Magnetic Resonance Imaging (MRI) is a non-invasive medical imaging technique that uses strong magnetic fields and radio waves to create detailed images of the body's internal structures. It is a powerful diagnostic tool that has revolutionized the field of medicine by providing healthcare professionals with a comprehensive view of the human body without the use of ionizing radiation.
Magnetic resonance imaging (MRI): Magnetic resonance imaging (MRI) is a medical imaging technique that uses powerful magnets and radio waves to create detailed images of the inside of the body. It relies on the principles of nuclear magnetic resonance, where atomic nuclei align with a magnetic field and emit signals when perturbed by radio waves.
Maxwell's Equations: Maxwell's equations are a set of four fundamental equations that describe the relationships between electric and magnetic fields and electric charges and currents. These equations form the foundation of classical electromagnetism and are essential for understanding various electromagnetic phenomena.
MRI: MRI, or Magnetic Resonance Imaging, is a non-invasive medical imaging technique that uses strong magnetic fields and radio waves to create detailed images of the body's internal structures. It is a powerful tool for diagnosing and monitoring various medical conditions, and its applications extend beyond the context of these specific physics topics.
Ohm's Law: Ohm's law is a fundamental principle in electrical engineering that describes the relationship between the voltage, current, and resistance in an electrical circuit. It states that the current flowing through a conductor is directly proportional to the voltage applied across it, and inversely proportional to the resistance of the conductor.
Right-hand rule: The right-hand rule is a mnemonic used to determine the direction of angular momentum vectors. It states that if you curl the fingers of your right hand in the direction of rotation, your thumb points in the direction of the angular momentum vector.
Right-Hand Rule: The right-hand rule is a mnemonic device used to determine the direction of various vector quantities in physics, such as magnetic fields, angular momentum, and the force on a moving charge in a magnetic field. It is a simple and intuitive way to visualize the relationship between these vectors and their associated directions.
Solenoid: A solenoid is a type of electromagnet consisting of a coil of wire wound into a tight spiral. When an electric current flows through the coil, it creates a magnetic field inside the solenoid, which can be used to produce a strong and uniform magnetic field in a specific region of space.
Step-down transformer: A step-down transformer is a device that decreases the voltage from the primary coil to the secondary coil while increasing the current. It is commonly used to convert high voltage electricity from power lines to a lower, safer voltage for use in homes and businesses.
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.
Transformer: A transformer is a device that transfers electrical energy from one alternating current (AC) circuit to another through the process of electromagnetic induction, without the need for direct electrical connection. It is a crucial component in the transmission and distribution of electrical power, as well as in various electronic devices.
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 used to quantify the amount of magnetic flux present in a magnetic field, and it plays a crucial role in understanding various electromagnetic phenomena.