chapter 23 magnetic flux and faraday’s law of induction

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Chapter 23 Magnetic Flux and Faraday’s Law of Induction

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Page 1: Chapter 23 Magnetic Flux and Faraday’s Law of Induction

Chapter 23

Magnetic Flux and Faraday’s Law of Induction

Page 2: 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

Page 3: Chapter 23 Magnetic Flux and Faraday’s Law of Induction

Units of Chapter 23

• Inductance

• RL Circuits

• Energy Stored in a Magnetic Field

• Transformers

Page 4: Chapter 23 Magnetic Flux and Faraday’s Law of Induction

23-1 Induced Electromotive ForceFaraday’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.

Page 5: Chapter 23 Magnetic Flux and Faraday’s Law of Induction

23-1 Induced Electromotive Force

• 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.

Page 6: Chapter 23 Magnetic Flux and Faraday’s Law of Induction

23-1 Induced Electromotive Force

Note the motion of the magnet in each image:

Page 7: Chapter 23 Magnetic Flux and Faraday’s Law of Induction

23-2 Magnetic Flux

Magnetic flux is used in the calculation of the induced emf.

Page 8: Chapter 23 Magnetic Flux and Faraday’s Law of Induction

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.

Page 9: Chapter 23 Magnetic Flux and Faraday’s Law of Induction

23-3 Faraday’s Law of Induction

There are many devices that operate on the basis of Faraday’s law.

An electric guitar pickup:

Page 10: Chapter 23 Magnetic Flux and Faraday’s Law of Induction

23-3 Faraday’s Law of Induction

Tape recorder:

Page 11: Chapter 23 Magnetic Flux and Faraday’s Law of Induction

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.

Page 12: Chapter 23 Magnetic Flux and Faraday’s Law of Induction

23-4 Lenz’s Law

This conducting rod completes the circuit. As it falls, the magnetic flux decreases, and a current is induced.

Page 13: Chapter 23 Magnetic Flux and Faraday’s Law of Induction

23-4 Lenz’s Law

The force due to the induced current is upward, slowing the fall.

Page 14: Chapter 23 Magnetic Flux and Faraday’s Law of Induction

23-4 Lenz’s Law

Currents can also flow in bulk conductors. These induced currents, called eddy currents, can be powerful brakes.

Page 15: Chapter 23 Magnetic Flux and Faraday’s Law of Induction

23-5 Mechanical Work and Electrical Energy

This diagram shows the variables we need to calculate the induced emf.

Page 16: Chapter 23 Magnetic Flux and Faraday’s Law of Induction

23-5 Mechanical Work and Electrical Energy

Change in flux:

Induced emf:

Electric field caused by the motion of the rod:

Page 17: Chapter 23 Magnetic Flux and Faraday’s Law of Induction

23-5 Mechanical Work and Electrical 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:

Page 18: Chapter 23 Magnetic Flux and Faraday’s Law of Induction

23-5 Mechanical Work and Electrical 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.

Page 19: Chapter 23 Magnetic Flux and Faraday’s Law of Induction

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.

Page 20: Chapter 23 Magnetic Flux and Faraday’s Law of Induction

23-6 Generators and Motors

The induced emf in a rotating coil varies sinusoidally:

Page 21: Chapter 23 Magnetic Flux and Faraday’s Law of Induction

23-6 Generators and Motors

An electric motor is exactly the opposite of a generator – it uses the torque on a current loop to create mechanical energy.

Page 22: Chapter 23 Magnetic Flux and Faraday’s Law of Induction

23-7 Inductance

When the switch is closed in this circuit, a current is established that increases with time.

Page 23: Chapter 23 Magnetic Flux and Faraday’s Law of Induction

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,

Page 24: Chapter 23 Magnetic Flux and Faraday’s Law of Induction

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.

Page 25: Chapter 23 Magnetic Flux and Faraday’s Law of Induction

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.

Page 26: Chapter 23 Magnetic Flux and Faraday’s Law of Induction

23-8 RL Circuits

This shows the current in an RL circuit as a function of time.

The time constant is:

Page 27: Chapter 23 Magnetic Flux and Faraday’s Law of Induction

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:

Page 28: Chapter 23 Magnetic Flux and Faraday’s Law of Induction

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.

Page 29: Chapter 23 Magnetic Flux and Faraday’s Law of Induction

23-10 Transformers

A transformer is used to change voltage in an alternating current from one value to another.

Page 30: Chapter 23 Magnetic Flux and Faraday’s Law of Induction

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.

Page 31: Chapter 23 Magnetic Flux and Faraday’s Law of Induction

23-10 Transformers

The power in both circuits must be the same; therefore, if the voltage is lower, the current must be higher.

Page 32: Chapter 23 Magnetic Flux and Faraday’s Law of Induction

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:

Page 33: Chapter 23 Magnetic Flux and Faraday’s Law of Induction

Summary of Chapter 23

• 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.

Page 34: Chapter 23 Magnetic Flux and Faraday’s Law of Induction

Summary of Chapter 23

• Definition of inductance:

• Inductance of a solenoid:

• An RL circuit has a characteristic time constant:

Page 35: Chapter 23 Magnetic Flux and Faraday’s Law of Induction

Summary of Chapter 23

• Current in an RL circuit after closing the switch:

• Magnetic energy density:

• Transformer equation: