Chapter 23 - PowerPoint Presentation for College Physics

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Lecture Outline

Chapter 23

Physics, 4th Edition

James S. Walker


Chapter 23

Magnetic Flux and Faraday’s

Law of Induction


Units of Chapter 23

• Induced Electromotive Force

• Magnetic Flux

• Faraday’s Law of Induction

• Lenz’s Law

• Mechanical Work and Electrical Energy

• Generators and Motors


Units of Chapter 23

• Inductance

• RL Circuits

• Energy Stored in a Magnetic Field

• Transformers


23-1 Induced Electromotive Force

Faraday’s experiment: closing the switch in the

primary circuit induces a current in the

secondary circuit, but only while the current in

the primary circuit is changing.



• The current in the secondary circuit is zero as

long as the current in the primary circuit, and

therefore the magnetic field in the iron bar, is not

changing.

• Current flows in the secondary circuit while the

current in the primary is changing. It flows in

opposite directions depending on whether the

magnetic field is increasing or decreasing.

• The magnitude of the induced current is

proportional to the rate at which the magnetic

field is changing.



Note the motion of the magnet in each image:


23-2 Magnetic Flux

Magnetic flux is used

in the calculation of the

induced emf.


23-3 Faraday’s Law of Induction

Faraday’s law: An emf is induced only when the

magnetic flux through a loop changes with time.



There are many devices that operate on the

basis of Faraday’s law.

An electric guitar

pickup:



Tape recorder:


23-4 Lenz’s LawLenz’s Law

An induced current always flows in a direction

that opposes the change that caused it.

Therefore, if the magnetic field is increasing, the

magnetic field created by the induced current will

be in the opposite direction; if decreasing, it will

be in the same direction.


23-4 Lenz’s Law

This conducting rod

completes the circuit.

As it falls, the magnetic

flux decreases, and a

current is induced.


23-4 Lenz’s Law

The force due to the

induced current is

upward, slowing the fall.


23-4 Lenz’s Law

Currents can also flow in

bulk conductors. These

induced currents, called eddy

currents, can be powerful

brakes.


23-5 Mechanical Work and Electrical

Energy

This diagram shows the variables we need to

calculate the induced emf.



Energy

Change in flux:

Induced emf:

Electric field caused by the motion of the

rod:



Energy

If the rod is to move at a constant speed, an

external force must be exerted on it. This force

should have equal magnitude and opposite

direction to the magnetic force:



Energy

The mechanical power delivered by the

external force is:

Compare this to the electrical power in the

light bulb:

Therefore, mechanical power has been

converted directly into electrical power.


23-6 Generators and Motors

An electric generator converts mechanical

energy into electric energy:

An outside source of

energy is used to

turn the coil, thereby

generating electricity.



The induced emf in a rotating coil varies

sinusoidally:



An electric motor is exactly the opposite of a

generator – it uses the torque on a current loop

to create mechanical energy.


23-7 Inductance

When the switch is closed in this circuit, a

current is established that increases with

time.


23-7 Inductance

Inductance is the proportionality constant that

tells us how much emf will be induced for a

given rate of change in current:

Solving for L,


23-7 Inductance

Given the definition of inductance, the

inductance of a solenoid can be calculated:

When used in a circuit, such a solenoid (or

other coil) is called an inductor.


23-8 RL Circuits

When the switch is closed, the current

immediately starts to increase. The back emf in

the inductor is large, as the current is

changing rapidly. As time goes on, the current

increases more slowly, and the potential

difference across the inductor decreases.


23-8 RL Circuits

This shows the current in an RL circuit as a

function of time.

The time constant is:


23-9 Energy Stored in a Magnetic Field

It takes energy to establish a current in an

inductor; this energy is stored in the inductor’s

magnetic field.

Considering the emf needed to establish a

particular current, and the power involved, we

find:


23-9 Energy Stored in a Magnetic Field

We know the inductance of a solenoid; therefore,

the magnetic energy stored in a solenoid is:

Dividing by the volume to find the energy

density gives:

This result is valid for any magnetic field,

regardless of source.


23-10 Transformers

A transformer is used to change voltage in an

alternating current from one value to another.


23-10 Transformers

By applying Faraday’s law of induction to both

coils, we find:

Here, p stands for the primary coil and s the

secondary.


23-10 Transformers

The power in both circuits must be the same;

therefore, if the voltage is lower, the current

must be higher.


Summary of Chapter 23

• A changing magnetic field can induce a current

in a circuit. The magnitude of the induced

current depends on the rate of change of the

magnetic field.

• Magnetic flux:

• Faraday’s law gives the induced emf:



• Lenz’s law: an induced current flows in the

direction that opposes the change that created

the current.

• Motional emf:

• emf produced by a generator:

• An electric motor is basically a generator

operated in reverse.

• Inductance occurs when a coil with a changing

current induces an emf in itself.



• Definition of inductance:

• Inductance of a solenoid:

• An RL circuit has a characteristic time

constant:



• Current in an RL circuit after closing the switch:

• Magnetic energy density:

• Transformer equation:

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Chapter 23 - PowerPoint Presentation for College Physics