1. Michael Faraday discovered the principles of electromagnetic induction in the early 1830s through experiments showing that a changing magnetic field can induce an electromotive force (emf) in a nearby conductor.
2. According to Faraday's law, an emf is induced in a closed loop of conductor when there is a change in the magnetic flux through the loop. The magnitude of the induced emf is proportional to the rate of change of the magnetic flux.
3. Self-induction describes the phenomenon of induction within a single circuit - as the current in a circuit changes, it induces its own opposing emf through its own magnetic field according to Lenz's law. This effect is quantified by the circuit's inductance
1. Michael Faraday discovered the principles of electromagnetic induction in the early 19th century through experiments showing that a changing magnetic field can induce an electromotive force (emf) in a nearby conductor.
2. Faraday's law of induction states that the magnitude of the induced emf is proportional to the rate of change of the magnetic flux through a circuit.
3. Generators and motors operate based on Faraday's law - a rotating coil of wire inside a magnetic field will experience a changing magnetic flux, inducing an emf to generate electricity in a generator, or experience a torque to cause rotation as a motor.
Faraday's law of induction states that a changing magnetic field induces an electromotive force (emf) in a nearby conductor. Michael Faraday discovered this phenomenon through experiments in 1831. Specifically, he found that moving a magnet toward or away from a coil of wire induces a temporary current in the coil. This led to the development of Faraday's law, which describes the relationship between the induced emf and the rate of change of the magnetic flux through a circuit. Applications of Faraday's law include electric generators, motors, and eddy current brakes.
Faraday's laws of electromagnetic induction describe how a changing magnetic field can induce an electromotive force (EMF) in a conductor. This is the operating principle behind electric generators and transformers. The document discusses Faraday's experiments demonstrating electromagnetic induction, his laws, self and mutual inductance, generation of sinusoidal voltages, phasor representation, and introduction to three-phase systems and electric grids. Key points covered include Faraday's law of induction, the relationship between induced EMF and rate of change of magnetic flux, how inductance opposes changes in current, and generation of sinusoidal AC voltages through rotating coils in magnetic fields.
Experiments in 1831 by Faraday and Henry showed that an emf can be induced in a circuit by a changing magnetic field. This led to the discovery of electromagnetic induction and Faraday's Law of Induction. According to Faraday's law, an induced emf is produced by the time rate of change of the magnetic flux through a circuit. Lenz's law describes how the direction of the induced current will be such that it creates an opposing magnetic field to the change that created it.
This document discusses inductance and induced electromotive force (emf). It explains that an induced emf is generated in a conductor when it moves through a magnetic field, and that changing the magnetic flux through a coil can induce an emf. It also states that an induced electric field is produced by a changing magnetic flux according to Faraday's law, and that this induced electric field is what drives the motion of conduction electrons. The document provides examples of inductance, self-inductance, and mutual inductance, and discusses how transformers use inductance to change voltages.
Michael Faraday was a British physicist and chemist in the 19th century who made many contributions to the field of electromagnetism. Some of his most important discoveries include the principles of electromagnetic induction, which established that a changing magnetic field can generate an electric current. He invented the electric motor, generator, and transformer based on these principles. Faraday established the laws of electrolysis through his experiments with electrolysis.
1. Michael Faraday discovered electromagnetic induction in 1831 when he found that a changing magnetic field can generate an electric current.
2. According to Faraday's laws of electromagnetic induction, a changing magnetic flux induces an electromotive force (emf) in a circuit. The magnitude of the induced emf is directly proportional to the rate of change of magnetic flux through the circuit.
3. Lenz's law states that the direction of the induced current is such that it creates its own magnetic field to oppose the original change in magnetic flux that created it.
1. Michael Faraday discovered the principles of electromagnetic induction in the early 19th century through experiments showing that a changing magnetic field can induce an electromotive force (emf) in a nearby conductor.
2. Faraday's law of induction states that the magnitude of the induced emf is proportional to the rate of change of the magnetic flux through a circuit.
3. Generators and motors operate based on Faraday's law - a rotating coil of wire inside a magnetic field will experience a changing magnetic flux, inducing an emf to generate electricity in a generator, or experience a torque to cause rotation as a motor.
Faraday's law of induction states that a changing magnetic field induces an electromotive force (emf) in a nearby conductor. Michael Faraday discovered this phenomenon through experiments in 1831. Specifically, he found that moving a magnet toward or away from a coil of wire induces a temporary current in the coil. This led to the development of Faraday's law, which describes the relationship between the induced emf and the rate of change of the magnetic flux through a circuit. Applications of Faraday's law include electric generators, motors, and eddy current brakes.
Faraday's laws of electromagnetic induction describe how a changing magnetic field can induce an electromotive force (EMF) in a conductor. This is the operating principle behind electric generators and transformers. The document discusses Faraday's experiments demonstrating electromagnetic induction, his laws, self and mutual inductance, generation of sinusoidal voltages, phasor representation, and introduction to three-phase systems and electric grids. Key points covered include Faraday's law of induction, the relationship between induced EMF and rate of change of magnetic flux, how inductance opposes changes in current, and generation of sinusoidal AC voltages through rotating coils in magnetic fields.
Experiments in 1831 by Faraday and Henry showed that an emf can be induced in a circuit by a changing magnetic field. This led to the discovery of electromagnetic induction and Faraday's Law of Induction. According to Faraday's law, an induced emf is produced by the time rate of change of the magnetic flux through a circuit. Lenz's law describes how the direction of the induced current will be such that it creates an opposing magnetic field to the change that created it.
This document discusses inductance and induced electromotive force (emf). It explains that an induced emf is generated in a conductor when it moves through a magnetic field, and that changing the magnetic flux through a coil can induce an emf. It also states that an induced electric field is produced by a changing magnetic flux according to Faraday's law, and that this induced electric field is what drives the motion of conduction electrons. The document provides examples of inductance, self-inductance, and mutual inductance, and discusses how transformers use inductance to change voltages.
Michael Faraday was a British physicist and chemist in the 19th century who made many contributions to the field of electromagnetism. Some of his most important discoveries include the principles of electromagnetic induction, which established that a changing magnetic field can generate an electric current. He invented the electric motor, generator, and transformer based on these principles. Faraday established the laws of electrolysis through his experiments with electrolysis.
1. Michael Faraday discovered electromagnetic induction in 1831 when he found that a changing magnetic field can generate an electric current.
2. According to Faraday's laws of electromagnetic induction, a changing magnetic flux induces an electromotive force (emf) in a circuit. The magnitude of the induced emf is directly proportional to the rate of change of magnetic flux through the circuit.
3. Lenz's law states that the direction of the induced current is such that it creates its own magnetic field to oppose the original change in magnetic flux that created it.
1. Electromagnetic induction is the process of using a changing magnetic field to induce a voltage in a conductor. This occurs when the magnetic flux through a loop of wire changes due to the relative motion of a magnet or changes in the strength of the magnetic field.
2. Michael Faraday discovered electromagnetic induction in 1831 through experiments showing that a changing magnetic field can generate an electric current in a nearby wire. This principle is applied in devices like generators, transformers, and inductive chargers.
3. Some key requirements for induction to occur are that the conductor be perpendicular to magnetic field lines and that the magnetic flux through the loop of wire must be changing for a voltage to be induced.
Electromagnetic induction occurs when a changing magnetic field induces a current in a conductor. Magnetic flux is the measure of the magnetic field passing through an area. Faraday's law states that an electromotive force (EMF) is induced in a conductor when there is a change in magnetic flux over time. Transformers use this principle to change voltage levels using a primary and secondary coil wound around an iron core. Lenz's law describes how the induced current will flow in a direction that creates an opposing magnetic field to the changing field that created it.
- Magnetic flux (ΦB) is a measure of magnetic field strength over an area, measured in webers (Wb). ΦB = BA, where B is magnetic field strength and A is area.
- According to Faraday's law of induction, any change in magnetic flux over time induces a voltage in a circuit. The faster the change, the greater the induced voltage.
- Lenz's law states that an induced current will flow in a direction that opposes the change causing it, in order to conserve energy. This explains the negative sign in Faraday's law.
electromagnetic Induction and application.pptKevinMulyadi
1) Electromagnetic induction occurs when a magnetic flux through a region changes over time, inducing an electromotive force (emf) in that region.
2) Faraday's law of induction states that the induced emf in a coil is proportional to the rate of change of the magnetic flux through the coil. A faster change in flux induces a greater emf.
3) Lenz's law describes the direction of the induced current: the induced current will flow such that its magnetic field opposes the change producing it, in accordance with the law of conservation of energy.
This document provides an overview of chapter 22 on electromagnetic induction. It discusses key concepts such as magnetic flux, Faraday's law of induction, Lenz's law, and applications including electric generators. The chapter covers how changing magnetic fields can induce emfs and currents in conductors based on Faraday's law. Lenz's law describes how the direction of induced currents will oppose the change that created them. Applications discussed include the reproduction of sound and electric generators.
The document summarizes key concepts about electromagnetic induction, including:
- Electromagnetic induction occurs when a magnet moves in and out of a solenoid, cutting the magnetic flux and inducing a current in the wire coil.
- Faraday's law and Lenz's law govern the direction and magnitude of induced currents.
- An AC generator uses the principle of electromagnetic induction to generate an alternating current through the rotation of a coil within a magnetic field.
- Transformers are used to change the voltage of an AC supply through electromagnetic induction between a primary and secondary coil.
- Electromagnetic induction is the process of generating current through a wire in a changing magnetic field. When a wire moves perpendicular to a magnetic field, charges in the wire move and create an induced electromotive force (EMF).
- Transformers use electromagnetic induction to increase or decrease alternating current voltages. They have primary and secondary coils wound around an iron core. The ratio of turns determines the ratio of voltages.
- Lenz's law states that the direction of the induced current is such that the magnetic field it creates opposes the original change in magnetic flux that caused it. This induced magnetic field allows transformers, motors, and generators to function.
1. The document discusses Michael Faraday's discovery of electromagnetic induction and the principles of inductance. It summarizes Faraday's experiments showing that a changing magnetic field can induce an electromotive force (EMF) in a nearby conductor.
2. It then explains Faraday's Law of Induction, which states that the induced EMF in a conductor is proportional to the rate of change of magnetic flux through the conductor. It also discusses Lenz's Law regarding the direction of induced current.
3. Finally, it provides examples of applications that utilize electromagnetic induction, including electric generators, induction stoves, and transformers.
1. Michael Faraday discovered electromagnetic induction in 1831 through experiments showing that a changing magnetic field can induce an electric current in a nearby conductor.
2. Faraday's law of induction states that the induced electromotive force (emf) in a conductor is equal to the rate of change of magnetic flux through the conductor.
3. This discovery established the basis for technologies such as electric generators, transformers, electric motors, and inductors which are crucial components of modern electric power systems and electronics.
1. Michael Faraday discovered electromagnetic induction in 1831 through experiments showing that a changing magnetic field can induce an electric current in a nearby conductor.
2. Faraday's law of induction states that the induced electromotive force (emf) in a conductor is equal to the rate of change of magnetic flux through the conductor.
3. This discovery established the basis for technologies such as electric generators, transformers, electric motors, and inductors which are crucial components of modern electric power systems and electronics.
Electromagnetic induction class 10 ICSE.pptxnysa tutorial
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1. Electromagnetic induction occurs when a magnetic flux through a circuit changes over time, inducing an emf and current.
2. Faraday's experiments demonstrated this effect and led to his laws of electromagnetic induction.
3. Lenz's law states that the direction of induced current will be such that it creates magnetic fields opposing the change producing it.
1. Electromagnetic induction occurs when a magnetic flux through a circuit changes, inducing an emf and current.
2. Faraday's experiments demonstrated this effect and led to his laws of induction.
3. Lenz's law states that the direction of induced current will oppose the change producing it, in accordance with the law of conservation of energy.
1. Electromagnetic induction occurs when a magnetic flux passes through a circuit, inducing an emf and current. This can be caused by changing the magnetic field strength, coil area, or orientation to the field.
2. Faraday's experiments demonstrated induction and led to his laws: an emf is induced by a changing magnetic flux, and the magnitude of induced emf is proportional to the rate of change of flux.
3. Lenz's law states that the direction of induced current will oppose the change producing it, in accordance with the law of conservation of energy.
1. Electromagnetic induction occurs when a changing magnetic flux induces an electromotive force (emf) in a circuit. This can be caused by changing the magnetic field strength, coil area, or relative orientation between the coil and magnetic field.
2. Faraday's experiments demonstrated that a changing magnetic flux induces a current in a circuit. His laws of electromagnetic induction state that an emf is induced proportional to the rate of change of magnetic flux through a circuit.
3. Lenz's law specifies that the induced current will flow in a direction to oppose the change producing it, in accordance with the law of conservation of energy.
This document summarizes key concepts related to electromagnetic induction:
1. It defines magnetic flux and describes how it can be changed by altering the magnetic field strength, coil area, or orientation to the field.
2. It outlines Faraday's experiments which demonstrated that a changing magnetic flux induces an electromotive force (emf) in a circuit.
3. It states Faraday's laws of induction and Lenz's law, describing the direction of the induced current.
4. It provides various methods for inducing an emf, including changing the magnetic field, coil area or orientation, and describes applications like generators and eddy currents.
This document discusses electromagnetic induction and self-induced electromotive force (EMF). It defines electromagnetic induction as the phenomenon of producing an EMF and current in a conductor when the magnetic flux through the conductor changes. An EMF can be induced dynamically via motion in a magnetic field, or statically if the field changes while the conductor is stationary. Self-induced EMF occurs when the current in a coil changes, altering the coil's self-generated magnetic flux and inducing an opposing EMF according to Lenz's law. The magnitude of self-induced EMF is equal to the negative of the rate of change of flux linkage over time. The coefficient of self-inductance L quantifies a coil's ability to
The document discusses motional electromotive force (emf) generated when a conductor moves through a magnetic field. It explains that as the conductor moves, a potential difference is created between its ends due to the separation of positive and negative charges. This potential difference, known as motional emf, is equal to the product of the magnetic field strength, length of the conductor, and its velocity perpendicular to the field. The document also provides examples of how motional emf causes induced currents in circuits involving moving conductors in magnetic fields.
- A changing magnetic field induces an electromotive force (emf) in a closed circuit according to Faraday's law of induction.
- Faraday's law states that the induced emf is proportional to the rate of change of the magnetic flux through the circuit.
- Lenz's law describes the direction of the induced current: it will flow such that its magnetic field opposes the change creating it.
Batteries -Introduction – Types of Batteries – discharging and charging of battery - characteristics of battery –battery rating- various tests on battery- – Primary battery: silver button cell- Secondary battery :Ni-Cd battery-modern battery: lithium ion battery-maintenance of batteries-choices of batteries for electric vehicle applications.
Fuel Cells: Introduction- importance and classification of fuel cells - description, principle, components, applications of fuel cells: H2-O2 fuel cell, alkaline fuel cell, molten carbonate fuel cell and direct methanol fuel cells.
A SYSTEMATIC RISK ASSESSMENT APPROACH FOR SECURING THE SMART IRRIGATION SYSTEMSIJNSA Journal
The smart irrigation system represents an innovative approach to optimize water usage in agricultural and landscaping practices. The integration of cutting-edge technologies, including sensors, actuators, and data analysis, empowers this system to provide accurate monitoring and control of irrigation processes by leveraging real-time environmental conditions. The main objective of a smart irrigation system is to optimize water efficiency, minimize expenses, and foster the adoption of sustainable water management methods. This paper conducts a systematic risk assessment by exploring the key components/assets and their functionalities in the smart irrigation system. The crucial role of sensors in gathering data on soil moisture, weather patterns, and plant well-being is emphasized in this system. These sensors enable intelligent decision-making in irrigation scheduling and water distribution, leading to enhanced water efficiency and sustainable water management practices. Actuators enable automated control of irrigation devices, ensuring precise and targeted water delivery to plants. Additionally, the paper addresses the potential threat and vulnerabilities associated with smart irrigation systems. It discusses limitations of the system, such as power constraints and computational capabilities, and calculates the potential security risks. The paper suggests possible risk treatment methods for effective secure system operation. In conclusion, the paper emphasizes the significant benefits of implementing smart irrigation systems, including improved water conservation, increased crop yield, and reduced environmental impact. Additionally, based on the security analysis conducted, the paper recommends the implementation of countermeasures and security approaches to address vulnerabilities and ensure the integrity and reliability of the system. By incorporating these measures, smart irrigation technology can revolutionize water management practices in agriculture, promoting sustainability, resource efficiency, and safeguarding against potential security threats.
1. Electromagnetic induction is the process of using a changing magnetic field to induce a voltage in a conductor. This occurs when the magnetic flux through a loop of wire changes due to the relative motion of a magnet or changes in the strength of the magnetic field.
2. Michael Faraday discovered electromagnetic induction in 1831 through experiments showing that a changing magnetic field can generate an electric current in a nearby wire. This principle is applied in devices like generators, transformers, and inductive chargers.
3. Some key requirements for induction to occur are that the conductor be perpendicular to magnetic field lines and that the magnetic flux through the loop of wire must be changing for a voltage to be induced.
Electromagnetic induction occurs when a changing magnetic field induces a current in a conductor. Magnetic flux is the measure of the magnetic field passing through an area. Faraday's law states that an electromotive force (EMF) is induced in a conductor when there is a change in magnetic flux over time. Transformers use this principle to change voltage levels using a primary and secondary coil wound around an iron core. Lenz's law describes how the induced current will flow in a direction that creates an opposing magnetic field to the changing field that created it.
- Magnetic flux (ΦB) is a measure of magnetic field strength over an area, measured in webers (Wb). ΦB = BA, where B is magnetic field strength and A is area.
- According to Faraday's law of induction, any change in magnetic flux over time induces a voltage in a circuit. The faster the change, the greater the induced voltage.
- Lenz's law states that an induced current will flow in a direction that opposes the change causing it, in order to conserve energy. This explains the negative sign in Faraday's law.
electromagnetic Induction and application.pptKevinMulyadi
1) Electromagnetic induction occurs when a magnetic flux through a region changes over time, inducing an electromotive force (emf) in that region.
2) Faraday's law of induction states that the induced emf in a coil is proportional to the rate of change of the magnetic flux through the coil. A faster change in flux induces a greater emf.
3) Lenz's law describes the direction of the induced current: the induced current will flow such that its magnetic field opposes the change producing it, in accordance with the law of conservation of energy.
This document provides an overview of chapter 22 on electromagnetic induction. It discusses key concepts such as magnetic flux, Faraday's law of induction, Lenz's law, and applications including electric generators. The chapter covers how changing magnetic fields can induce emfs and currents in conductors based on Faraday's law. Lenz's law describes how the direction of induced currents will oppose the change that created them. Applications discussed include the reproduction of sound and electric generators.
The document summarizes key concepts about electromagnetic induction, including:
- Electromagnetic induction occurs when a magnet moves in and out of a solenoid, cutting the magnetic flux and inducing a current in the wire coil.
- Faraday's law and Lenz's law govern the direction and magnitude of induced currents.
- An AC generator uses the principle of electromagnetic induction to generate an alternating current through the rotation of a coil within a magnetic field.
- Transformers are used to change the voltage of an AC supply through electromagnetic induction between a primary and secondary coil.
- Electromagnetic induction is the process of generating current through a wire in a changing magnetic field. When a wire moves perpendicular to a magnetic field, charges in the wire move and create an induced electromotive force (EMF).
- Transformers use electromagnetic induction to increase or decrease alternating current voltages. They have primary and secondary coils wound around an iron core. The ratio of turns determines the ratio of voltages.
- Lenz's law states that the direction of the induced current is such that the magnetic field it creates opposes the original change in magnetic flux that caused it. This induced magnetic field allows transformers, motors, and generators to function.
1. The document discusses Michael Faraday's discovery of electromagnetic induction and the principles of inductance. It summarizes Faraday's experiments showing that a changing magnetic field can induce an electromotive force (EMF) in a nearby conductor.
2. It then explains Faraday's Law of Induction, which states that the induced EMF in a conductor is proportional to the rate of change of magnetic flux through the conductor. It also discusses Lenz's Law regarding the direction of induced current.
3. Finally, it provides examples of applications that utilize electromagnetic induction, including electric generators, induction stoves, and transformers.
1. Michael Faraday discovered electromagnetic induction in 1831 through experiments showing that a changing magnetic field can induce an electric current in a nearby conductor.
2. Faraday's law of induction states that the induced electromotive force (emf) in a conductor is equal to the rate of change of magnetic flux through the conductor.
3. This discovery established the basis for technologies such as electric generators, transformers, electric motors, and inductors which are crucial components of modern electric power systems and electronics.
1. Michael Faraday discovered electromagnetic induction in 1831 through experiments showing that a changing magnetic field can induce an electric current in a nearby conductor.
2. Faraday's law of induction states that the induced electromotive force (emf) in a conductor is equal to the rate of change of magnetic flux through the conductor.
3. This discovery established the basis for technologies such as electric generators, transformers, electric motors, and inductors which are crucial components of modern electric power systems and electronics.
Electromagnetic induction class 10 ICSE.pptxnysa tutorial
Hello our respected institutions and faculties
if you want to buy Editable materials (6 to 12th/Foundation/JEE/NEET/CET) for your institution
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*CBSE 6 TO 10 TOPICWISE PER CHAPTER 100 QUESTION WITH ANSWER MATHEMATICS & SCIENCE & SST (Biology,Physics,Chemistry & Social studies)* Editable ms word
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For Sample Massage me .
1. Electromagnetic induction occurs when a magnetic flux through a circuit changes over time, inducing an emf and current.
2. Faraday's experiments demonstrated this effect and led to his laws of electromagnetic induction.
3. Lenz's law states that the direction of induced current will be such that it creates magnetic fields opposing the change producing it.
1. Electromagnetic induction occurs when a magnetic flux through a circuit changes, inducing an emf and current.
2. Faraday's experiments demonstrated this effect and led to his laws of induction.
3. Lenz's law states that the direction of induced current will oppose the change producing it, in accordance with the law of conservation of energy.
1. Electromagnetic induction occurs when a magnetic flux passes through a circuit, inducing an emf and current. This can be caused by changing the magnetic field strength, coil area, or orientation to the field.
2. Faraday's experiments demonstrated induction and led to his laws: an emf is induced by a changing magnetic flux, and the magnitude of induced emf is proportional to the rate of change of flux.
3. Lenz's law states that the direction of induced current will oppose the change producing it, in accordance with the law of conservation of energy.
1. Electromagnetic induction occurs when a changing magnetic flux induces an electromotive force (emf) in a circuit. This can be caused by changing the magnetic field strength, coil area, or relative orientation between the coil and magnetic field.
2. Faraday's experiments demonstrated that a changing magnetic flux induces a current in a circuit. His laws of electromagnetic induction state that an emf is induced proportional to the rate of change of magnetic flux through a circuit.
3. Lenz's law specifies that the induced current will flow in a direction to oppose the change producing it, in accordance with the law of conservation of energy.
This document summarizes key concepts related to electromagnetic induction:
1. It defines magnetic flux and describes how it can be changed by altering the magnetic field strength, coil area, or orientation to the field.
2. It outlines Faraday's experiments which demonstrated that a changing magnetic flux induces an electromotive force (emf) in a circuit.
3. It states Faraday's laws of induction and Lenz's law, describing the direction of the induced current.
4. It provides various methods for inducing an emf, including changing the magnetic field, coil area or orientation, and describes applications like generators and eddy currents.
This document discusses electromagnetic induction and self-induced electromotive force (EMF). It defines electromagnetic induction as the phenomenon of producing an EMF and current in a conductor when the magnetic flux through the conductor changes. An EMF can be induced dynamically via motion in a magnetic field, or statically if the field changes while the conductor is stationary. Self-induced EMF occurs when the current in a coil changes, altering the coil's self-generated magnetic flux and inducing an opposing EMF according to Lenz's law. The magnitude of self-induced EMF is equal to the negative of the rate of change of flux linkage over time. The coefficient of self-inductance L quantifies a coil's ability to
The document discusses motional electromotive force (emf) generated when a conductor moves through a magnetic field. It explains that as the conductor moves, a potential difference is created between its ends due to the separation of positive and negative charges. This potential difference, known as motional emf, is equal to the product of the magnetic field strength, length of the conductor, and its velocity perpendicular to the field. The document also provides examples of how motional emf causes induced currents in circuits involving moving conductors in magnetic fields.
- A changing magnetic field induces an electromotive force (emf) in a closed circuit according to Faraday's law of induction.
- Faraday's law states that the induced emf is proportional to the rate of change of the magnetic flux through the circuit.
- Lenz's law describes the direction of the induced current: it will flow such that its magnetic field opposes the change creating it.
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2. Michael Faraday
1791 – 1867
Great experimental
physicist
Contributions to early
electricity include
Invention of motor,
generator, and
transformer
Electromagnetic
induction
Laws of electrolysis
3. Induction
An induced current is produced by a
changing magnetic field
There is an induced emf associated with
the induced current
A current can be produced without a
battery present in the circuit
Faraday’s Law of Induction describes
the induced emf
4. EMF Produced by a
Changing Magnetic Field, 1
A loop of wire is connected to a sensitive ammeter
When a magnet is moved toward the loop, the
ammeter deflects
The deflection indicates a current induced in the wire
5. EMF Produced by a
Changing Magnetic Field, 2
When the magnet is held stationary, there is
no deflection of the ammeter
Therefore, there is no induced current
Even though the magnet is inside the loop
6. EMF Produced by a
Changing Magnetic Field, 3
The magnet is moved away from the loop
The ammeter deflects in the opposite
direction
7. EMF Produced by a Changing
Magnetic Field, Summary
The ammeter deflects when the magnet is
moving toward or away from the loop
The ammeter also deflects when the loop is
moved toward or away from the magnet
An electric current is set up in the coil as long
as relative motion occurs between the
magnet and the coil
This is the induced current that is produced by an
induced emf
8. Faraday’s Experiment –
Set Up
A primary coil is connected to
a switch and a battery
The wire is wrapped around
an iron ring
A secondary coil is also
wrapped around the iron ring
There is no battery present in
the secondary coil
The secondary coil is not
electrically connected to the
primary coil
9. Faraday’s Experiment –
Findings
At the instant the switch is closed, the
galvanometer (ammeter) needle deflects in
one direction and then returns to zero
When the switch is opened, the galvanometer
needle deflects in the opposite direction and
then returns to zero
The galvanometer reads zero when there is a
steady current or when there is no current in
the primary circuit
10. Faraday’s Experiment –
Conclusions
An electric current can be produced by a time-
varying magnetic field
This would be the current in the secondary circuit of
this experimental set-up
The induced current exists only for a short time
while the magnetic field is changing
This is generally expressed as: an induced
emf is produced in the secondary circuit by
the changing magnetic field
The actual existence of the magnetic field is not
sufficient to produce the induced emf, the field must
be changing
11. Magnetic Flux
To express
Faraday’s finding
mathematically, the
magnetic flux is
used
The flux depends on
the magnetic field
and the area:
B d
B A
12. Flux and Induced emf
An emf is induced in a circuit when the
magnetic flux through the surface
bounded by the circuit changes with
time
This summarizes Faraday’s experimental
results
13. Faraday’s Law – Statements
Faraday’s Law of Induction states that
the emf induced in a circuit is equal
to the time rate of change of the
magnetic flux through the circuit
Mathematically,
B
d
dt
14. Faraday’s Law –
Statements, cont
If the circuit consists of N identical and
concentric loops, and if the field lines
pass through all loops, the induced emf
becomes
The loops are in series, so the emfs in the
individual loops add to give the total emf
B
d
N
dt
15. Faraday’s Law – Example
Assume a loop
enclosing an area A
lies in a uniform
magnetic field
The magnetic flux
through the loop is
B = B A cos q
The induced emf is
cos
d
BA
dt
q
16. Ways of Inducing an emf
The magnitude of the field can change
with time
The area enclosed by the loop can
change with time
The angle q between the field and the
normal to the loop can change with time
Any combination of the above can occur
17. Applications of
Faraday’s Law – Pickup Coil
The pickup coil of an electric
guitar uses Faraday’s Law
The coil is placed near the
vibrating string and causes a
portion of the string to
become magnetized
When the string vibrates at
the some frequency, the
magnetized segment
produces a changing flux
through the coil
The induced emf is fed to an
amplifier
18. Motional emf
A motional emf is one
induced in a conductor
moving through a
magnetic field
The electrons in the
conductor experience
a force that is directed
along l
B q
F v B
19. Motional emf, cont
Under the influence of the force, the electrons
move to the lower end of the conductor and
accumulate there
As a result of the charge separation, an
electric field is produced inside the conductor
The charges accumulate at both ends of the
conductor until they are in equilibrium with
regard to the electric and magnetic forces
20. Motional emf, final
For equilibrium, q E = q v B or E = v B
A potential difference is maintained
between the ends of the conductor as
long as the conductor continues to
move through the uniform magnetic field
If the direction of the motion is reversed,
the polarity of the potential difference is
also reversed
21. Sliding Conducting Bar
A bar moving through a uniform field and the
equivalent circuit diagram
Assume the bar has zero resistance
The work done by the applied force appears as
internal energy in the resistor R
22. Sliding Conducting Bar, cont
The induced emf is
Since the resistance in the circuit is R,
the current is
B
d dx
B B v
dt dt
B v
I
R R
23. Sliding Conducting Bar,
Energy Considerations
The applied force does work on the
conducting bar
This moves the charges through a magnetic
field
The change in energy of the system during
some time interval must be equal to the
transfer of energy into the system by work
The power input is equal to the rate at which
energy is delivered to the resistor
2
app
F v I B v
R
24. AC Generators
Electric generators take
in energy by work and
transfer it out by
electrical transmission
The AC generator
consists of a loop of
wire rotated by some
external means in a
magnetic field
25. Induced emf
In an AC Generator
The induced emf in
the loops is
This is sinusoidal,
with max = N A B w
sin
B
d
N
dt
NAB t
w w
26. Lenz’ Law
Faraday’s Law indicates the induced
emf and the change in flux have
opposite algebraic signs
This has a physical interpretation that
has come to be known as Lenz’ Law
It was developed by a German
physicist, Heinrich Lenz
27. Lenz’ Law, cont
Lenz’ Law states the polarity of the
induced emf in a loop is such that it
produces a current whose magnetic
field opposes the change in magnetic
flux through the loop
The induced current tends to keep the
original magnetic flux through the circuit
from changing
28. Lenz’ Law – Example 1
When the magnet is moved toward the stationary
loop, a current is induced as shown in a
This induced current produces its own magnetic field
that is directed as shown in b to counteract the
increasing external flux
29. Lenz’ Law – Example 2
When the magnet is moved away the stationary loop,
a current is induced as shown in c
This induced current produces its own magnetic field
that is directed as shown in d to counteract the
decreasing external flux
30. Induced emf
and Electric Fields
An electric field is created in the conductor
as a result of the changing magnetic flux
Even in the absence of a conducting loop,
a changing magnetic field will generate an
electric field in empty space
This induced electric field has different
properties than a field produced by
stationary charges
31. Induced emf
and Electric Fields, cont
The emf for any closed path can be
expressed as the line integral of
over the path
Faraday’s Law can be written in a
general form
B
d
d
dt
E s
d
E s
32. Induced emf
and Electric Fields, final
The induced electric field is a
nonconservative field that is generated
by a changing magnetic field
The field cannot be an electrostatic field
because if the field were electrostatic,
and hence conservative, the line
integral would be zero and it isn’t
33. Self-Induction
When the switch is
closed, the current
does not
immediately reach
its maximum value
Faraday’s Law can
be used to describe
the effect
34. Self-Induction, 2
As the current increases with time, the
magnetic flux through the circuit loop
due to this current also increases with
time
The corresponding flux due to this
current also increases
This increasing flux creates an induced
emf in the circuit
35. Self-Inductance, 3
The direction of the induced emf is such that
it would cause an induced current in the loop
which would establish a magnetic field
opposing the change in the original magnetic
field
The direction of the induced emf is opposite
the direction of the emf of the battery
Sometimes called a back emf
This results in a gradual increase in the
current to its final equilibrium value
36. Self-Induction, 4
This effect is called self-inductance
Because the changing flux through the
circuit and the resultant induced emf arise
from the circuit itself
The emf L is called a self-induced
emf
37. Self-Inductance, Equations
An induced emf is always proportional
to the time rate of change of the current
L is a constant of proportionality called
the inductance of the coil
It depends on the geometry of the coil and
other physical characteristics
L
dI
L
dt
38. Inductance of a Coil
A closely spaced coil of N turns carrying
current I has an inductance of
The inductance is a measure of the
opposition to a change in current
Compared to resistance which was
opposition to the current
B
N
L
I dI dt
39. Inductance Units
The SI unit of inductance is a Henry (H)
Named for Joseph Henry
A
s
V
1
H
1
40. Joseph Henry
1797 – 1878
Improved the design of
the electromagnet
Constructed one of the
first motors
Discovered the
phenomena of self-
inductance
41. Inductance of a Solenoid
Assume a uniformly wound solenoid
having N turns and length l
Assume l is much greater than the radius
of the solenoid
The interior magnetic field is
o o
N
B nI I
42. Inductance of a Solenoid, cont
The magnetic flux through each turn is
Therefore, the inductance is
This shows that L depends on the
geometry of the object
B o
NA
BA I
2
o
B N A
N
L
I
43. RL Circuit, Introduction
A circuit element that has a large self-
inductance is called an inductor
The circuit symbol is
We assume the self-inductance of the
rest of the circuit is negligible compared
to the inductor
However, even without a coil, a circuit will
have some self-inductance
44. RL Circuit, Analysis
An RL circuit contains
an inductor and a
resistor
When the switch is
closed (at time t=0), the
current begins to
increase
At the same time, a
back emf is induced in
the inductor that
opposes the original
increasing current
45. RL Circuit, Analysis, cont
Applying Kirchhoff’s Loop Rule to the
previous circuit gives
Looking at the current, we find
0
dI
IR L
dt
1 Rt L
I e
R
46. RL Circuit, Analysis, Final
The inductor affects the current
exponentially
The current does not instantly increase
to its final equilibrium value
If there is no inductor, the exponential
term goes to zero and the current would
instantaneously reach its maximum
value as expected
47. RL Circuit, Time Constant
The expression for the current can also be
expressed in terms of the time constant, t, of
the circuit
where t = L / R
Physically, t is the time required for the
current to reach 63.2% of its maximum value
1 t
I t e
R
t
48. RL Circuit,
Current-Time Graph, 1
The equilibrium value
of the current is /R
and is reached as t
approaches infinity
The current initially
increases very rapidly
The current then
gradually approaches
the equilibrium value
49. RL Circuit,
Current-Time Graph, 2
The time rate of
change of the
current is a
maximum at t = 0
It falls off
exponentially as t
approaches infinity
In general,
t
dI
e
dt L
t
50. Energy in a Magnetic Field
In a circuit with an inductor, the battery
must supply more energy than in a
circuit without an inductor
Part of the energy supplied by the
battery appears as internal energy in
the resistor
The remaining energy is stored in the
magnetic field of the inductor
51. Energy in a
Magnetic Field, cont
Looking at this energy (in terms of rate)
I is the rate at which energy is being supplied by
the battery
I2R is the rate at which the energy is being
delivered to the resistor
Therefore, LI dI/dt must be the rate at which the
energy is being delivered to the inductor
2 dI
I I R LI
dt
52. Energy in a
Magnetic Field, final
Let U denote the energy stored in the
inductor at any time
The rate at which the energy is stored is
To find the total energy, integrate and
UB = ½ L I2
B
dU dI
LI
dt dt
53. Energy Density
of a Magnetic Field
Given U = ½ L I2,
Since Al is the volume of the solenoid, the
magnetic energy density, uB is
This applies to any region in which a
magnetic field exists
not just the solenoid
2
2
2
1
2 2
o
o o
B B
U n A A
n
2
2
B
o
U B
u
V
54. Inductance Example –
Coaxial Cable
Calculate L and
energy for the cable
The total flux is
Therefore, L is
The total energy is
ln
2 2
b
o o
B a
I I b
BdA dr
r a
ln
2
o
B b
L
I a
2
2
1
ln
2 4
o I b
U LI
a
55. Magnetic Levitation –
Repulsive Model
A second major model for magnetic
levitation is the EDS (electrodynamic
system) model
The system uses superconducting
magnets
This results in improved energy
effieciency
56. Magnetic Levitation –
Repulsive Model, 2
The vehicle carries a magnet
As the magnet passes over a metal plate that
runs along the center of the track, currents
are induced in the plate
The result is a repulsive force
This force tends to lift the vehicle
There is a large amount of metal required
Makes it very expensive
57. Japan’s Maglev Vehicle
The current is
induced by magnets
passing by coils
located on the side
of the railway
chamber
58. EDS Advantages
Includes a natural stabilizing feature
If the vehicle drops, the repulsion becomes
stronger, pushing the vehicle back up
If the vehicle rises, the force decreases
and it drops back down
Larger separation than EMS
About 10 cm compared to 10 mm
59. EDS Disadvantages
Levitation only exists while the train is in
motion
Depends on a change in the magnetic flux
Must include landing wheels for stopping and
starting
The induced currents produce a drag force as
well as a lift force
High speeds minimize the drag
Significant drag at low speeds must be overcome
every time the vehicle starts up