13.2 Lenz's Law
3 min read•june 24, 2024
is all about creating electricity from changing magnetic fields. ###'s_Law_0### tells us that the always opposes the change causing it, like a stubborn friend who always does the opposite of what you want.
helps us calculate the induced voltage, while Lenz's law explains its direction. This dance between electricity and magnetism is key to understanding how generators work and why your phone charger gets warm.
Lenz's Law and Electromagnetic Induction
Direction of induced current
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- Lenz's law states induced current in conductor opposes change in magnetic flux that caused it
- When magnetic flux through loop increases, induced current flows to create magnetic field opposing increase in flux
- When magnetic flux through loop decreases, induced current flows to create magnetic field opposing decrease in flux
- Bar magnet's north pole moved towards coil, induced current flows to create magnetic field with north pole facing approaching magnet, repelling it
- Bar magnet's north pole moved away from coil, induced current flows to create magnetic field with south pole facing receding magnet, attracting it
- The can be used to determine the direction of the induced current
Calculation of induced emf
- Faraday's law states magnitude of induced emf () in circuit directly proportional to rate of change of magnetic flux () through circuit
- Negative sign represents Lenz's law, indicating induced emf opposes change in flux
- For tightly wound coil with turns, induced emf given by:
- Magnetic flux through coil or given by:
- magnetic field strength
- of coil or
- angle between magnetic field and normal to coil's surface
- Combining equations, induced emf in coil or solenoid calculated as:
- (if changes with time)
- (if angle changes with time)
- (if area changes with time)
Lenz's law and energy conservation
- Lenz's law consequence of conservation of energy principle
- Induced current always flows in direction that opposes change in magnetic flux that caused it
- Opposition ensures energy conserved in system
- If induced current flowed in same direction as change in flux, it would amplify change, leading to ever-increasing flux and current, violating conservation of energy
- By opposing change in flux, induced current acts to minimize overall change in system
- Opposition converts some mechanical energy used to change flux into electrical energy in form of induced current
- Work done by external force to overcome opposing force due to induced current equal to electrical energy generated in circuit
- Demonstrates conservation of energy, as mechanical work converted into electrical energy
Magnetic Field Interactions
- represent the direction and strength of a magnetic field in space
- The created by the induced current interacts with the external magnetic field
- The magnetic dipole moment of a current loop determines its interaction with external magnetic fields
Key Terms to Review (27)
BA cos θ: BA cos θ is a term that represents the component of a magnetic field that is perpendicular to the area vector of a loop or circuit. It is a crucial concept in the understanding of Lenz's Law, which describes the direction of the induced current in an electromagnetic induction scenario.
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.
Cross-Sectional Area: The cross-sectional area of an object is the area of the surface perpendicular to the direction of the flow or motion. It is a measure of the size or magnitude of the object's interaction with the surrounding medium, and is an important parameter in various physical and engineering applications.
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 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: Electromotive force (EMF) is the voltage or potential difference generated in an electrical circuit, typically by a source of electrical energy such as a battery or generator. It is the driving force that causes electric charge to flow through a circuit, enabling the conversion of other forms of energy into electrical energy.
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.
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 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 Current: Induced current refers to the flow of electric charge that is generated within a conductor when it experiences a change in the magnetic field surrounding it. This phenomenon is a fundamental principle in electromagnetism and is the basis for many important applications, including the operation of electric generators, transformers, and various electromagnetic devices.
Induced Magnetic Field: An induced magnetic field is a magnetic field that is generated by the movement of an electric charge or by a changing electric field. This phenomenon is described by Faraday's law of electromagnetic induction, which states that a changing magnetic field can induce an electromotive force (EMF) in a conductor, leading to the creation of an induced magnetic field.
Lenz: Lenz's Law states that the direction of an induced current in a conductor due to a changing magnetic field is such that it creates a magnetic field opposing the change. This law ensures the conservation of energy in electromagnetic systems.
Lenz’s law: Lenz's Law states that the direction of an induced electric current will oppose the change in magnetic flux that caused it. This is a consequence of the conservation of energy.
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.
Mutual Inductance: Mutual inductance is a measure of the magnetic coupling between two electrical circuits or coils. It describes the amount of induced voltage in one circuit due to a changing current in another circuit, and it is a key concept in understanding the principles of electromagnetic induction.
Mutual inductance (M): Mutual inductance is the phenomenon where a change in current in one coil induces an electromotive force (EMF) in a nearby coil. It is quantified by the mutual inductance coefficient, $M$, which depends on the geometry and orientation of the coils.
N turns: N turns refers to the number of loops or coils of wire in an inductor or transformer. The number of turns in an electromagnetic device is a critical factor that determines its behavior and performance, particularly in the context of Lenz's Law.
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.
Right-hand rule 2: Right-hand rule 2 is a mnemonic used to determine the direction of the induced current when a conductor moves through a magnetic field. Point the thumb of your right hand in the direction of motion of the conductor, and your fingers in the direction of the magnetic field; your palm will face in the direction of the induced current.
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.
ε = -dΦ/dt: This term represents Faraday's law of electromagnetic induction, which states that the electromotive force (emf) induced in a circuit is proportional to the negative rate of change of the magnetic flux through the circuit. The term 'ε' represents the induced emf, and 'dΦ/dt' represents the rate of change of the magnetic flux Φ over time 't'.
ΦB: ΦB, also known as the magnetic flux, is a fundamental concept in the study of electromagnetic induction. It represents the total amount of magnetic field passing through a given surface or loop, and is a crucial factor in understanding Lenz's Law.