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Electromagnetic InductionChapter 20

Table of Contents

Section 1 Electricity from Magnetism

Section 2 Generators, Motors, and Mutual Inductance

Section 3 AC Circuits and Transformers

Section 4 Electromagnetic Waves




Chapter 20

Objectives

• Recognize that relative motion between a conductor and a magnetic field induces an emf in the conductor.

• Describe how the change in the number of magnetic field lines through a circuit loop affects the magnitude and direction of the induced electric current.

• Apply Lenz’s law and Faraday’s law of induction to solve problems involving induced emf and current.




Chapter 20

Electromagnetic Induction

• Electromagnetic induction is the process of creating a current in a circuit by a changing magnetic field.

• A change in the magnetic flux through a conductor induces an electric current in the conductor.

• The separation of charges by the magnetic force induces an emf.



Chapter 20

Electromagnetic Induction in a Circuit Loop





Chapter 20

Electromagnetic Induction, continued

• The angle between a magnetic field and a circuit affects induction.

• A change in the number of magnetic field lines induces a current.



Chapter 20

Ways of Inducing a Current in a Circuit


http://lcmrschooldistrict.com/roth/Physics_animate/Ch20/1-induce-current.swf

http://lcmrschooldistrict.com/roth/Physics_animate/Ch20/1-induce-current.swf




Chapter 20

Characteristics of Induced Current

• Lenz’s Law

The magnetic field of the induced current is in a direction to produce a field that opposes the change causing it.

• Note: the induced current does not oppose the applied field, but rather the change in the applied field.



Chapter 20

Lenz's Law for Determining the Direction of the Induced Current


http://lcmrschooldistrict.com/roth/Physics_animate/Ch20/1-Lenz-law.swf








Chapter 20

Characteristics of Induced Current, continued

• The magnitude of the induced emf can be predicted by Faraday’s law of magnetic induction.

• Faraday’s Law of Magnetic Induction

average induced emf = –the number of loops in the circuit

the time rate of change in the magnetic flux

– Memf Nt

•The magnetic flux is given by FM = ABcos .q




Chapter 20

Sample Problem

Induced emf and Current

A coil with 25 turns of wire is wrapped around a hollow tube with an area of 1.8 m2. Each turn has the same area as the tube. A uniform magnetic field is applied at a right angle to the plane of the coil. If the field increases uniformly from 0.00 T to 0.55 T in 0.85 s, find the magnitude of the induced emf in the coil. If the resistance in the coil is 2.5 Ω, find the magnitude of the induced current in the coil.




Chapter 20

Sample Problem, continued


1. Define

Given:

∆t = 0.85 s A = 1.8 m2 q = 0.0º

N = 25 turns R = 2.5 Ω

Bi = 0.00 T = 0.00 V•s/m2

Bf = 0.55 T = 0.55 V•s/m2

Unknown:

emf = ?

I = ?




Chapter 20


Induced emf and Current1. Define, continued

Diagram: Show the coil before and after the change in the magnetic field.




Chapter 20



2. Plan

Choose an equation or situation. Use Faraday’s law of magnetic induction to find the induced emf in the coil.

cos– –M

ABemf N N

t t

Substitute the induced emf into the definition of resistance to determine the induced

current in the coil.

emf

IR




Chapter 20



2. Plan, continued

Rearrange the equation to isolate the unknown. In this example, only the magnetic field strength changes with time. The other components (the coil area and the angle between the magnetic field and the coil) remain constant.

– cos

Bemf NA

t




Chapter 20


Induced emf and Current3. Calculate

Substitute the values into the equation and solve.

22

V•s0.55 – 0.00

m–(25)(1.8 m )(cos0.0º ) –29 V

(0.85 s)

–29 V–12 A

2.5 Ω

–29 V

–12 A

emf

I

emf

I




Chapter 20


Induced emf and Current4. Evaluate

The induced emf, and therefore the induced current, is directed through the coil so that the magnetic field produced by the induced current opposes the change in the applied magnetic field. For the diagram shown on the previous page, the induced magnetic field is directed to the right and the current that produces it is directed from left to right through the resistor.




Chapter 20

Objectives

• Describe how generators and motors operate.

• Explain the energy conversions that take place in generators and motors.

• Describe how mutual induction occurs in circuits.




Chapter 20

Generators and Alternating Current

• A generator is a machine that converts mechanical energy into electrical energy.

• Generators use induction to convert mechanical energy into electrical energy.

• A generator produces a continuously changing emf.



Chapter 20

Induction of an emf in an AC Generator




Chapter 20

Function of a Generator


http://lcmrschooldistrict.com/roth/Physics_animate/Ch20/2-generator-function.swf






Chapter 20

Generators and Alternating Current, continued

• Alternating current is an electric current that changes direction at regular intervals.

• Alternating current can be converted to direct current by using a device called a commutator to change the direction of the current.



Chapter 20

Comparing AC and DC Generators


http://lcmrschooldistrict.com/roth/Physics_animate/Ch20/2-ac-dc-generator.swf

http://lcmrschooldistrict.com/roth/Physics_animate/Ch20/2-ac-dc-generator.swf




Chapter 20

Motors

• Motors are machines that convert electrical energy to mechanical energy.

• Motors use an arrangement similar to that of generators.

• Back emf is the emf induced in a motor’s coil that tends to reduce the current in the coil of a motor.



Chapter 20

DC Motors


http://lcmrschooldistrict.com/roth/Physics_animate/Ch20/2-dc-motor.swf




Chapter 20

Mutual Inductance

• The ability of one circuit to induce an emf in a nearby circuit in the presence of a changing current is called mutual inductance.

• In terms of changing primary current, Faraday’s law is given by the following equation, where M is the mutual inductance:

– –M I

emf N Mt t



Chapter 20

Mutual Inductance


http://lcmrschooldistrict.com/roth/Physics_animate/Ch20/2-mutual-inductance.swf




Chapter 20

Objectives

• Distinguish between rms values and maximum values of current and potential difference.

• Solve problems involving rms and maximum values of current and emf for ac circuits.

• Apply the transformer equation to solve problems involving step-up and step-down transformers.




Chapter 20

Effective Current

• The root-mean-square (rms) current of a circuit is the value of alternating current that gives the same heating effect that the corresponding value of direct current does.

• rms Current

maxmax0.707

2rms

II I




Chapter 20

Effective Current, continued

• The rms current and rms emf in an ac circuit are important measures of the characteristics of an ac circuit.

• Resistance influences current in an ac circuit.



Chapter 20

rms Current


http://lcmrschooldistrict.com/roth/Physics_animate/Ch20/3-rms-current.swf




Chapter 20

Sample Problem

rms Current and emf

A generator with a maximum output emf of 205 V is connected to a 115 Ω resistor. Calculate the rms potential difference. Find the rms current through the resistor. Find the maximum ac current in the circuit.

1. Define

Given:

∆Vrms = 205 V R = 115 Ω

Unknown:

∆Vrms = ? Irms = ? Imax = ?




Chapter 20


rms Current and emf2. Plan

Choose an equation or situation. Use the equation for the rms potential difference to find ∆Vrms.

∆Vrms = 0.707 ∆Vmax

Rearrange the definition for resistance to calculate Irms.

rmsrms

VI

R

Use the equation for rms current to find Irms.

Irms = 0.707 Imax




Chapter 20


rms Current and emf2. Plan, continued

Rearrange the equation to isolate the unknown. Rearrange the equation relating rms current to maximum current so that maximum current is calculated.

max 0.707rmsI

I




Chapter 20


rms Current and emf3. Calculate

Substitute the values into the equation and solve.

max

(0.707)(205 V) 145 V

145 V1.26 A

115 Ω1.26 A

1.78 A0.707

rms

rms

V

I

I

4. Evaluate The rms values for emf and current are a little more than two-thirds the

maximum values, as expected.




Chapter 20

Transformers

• A transformer is a device that increases or decreases the emf of alternating current.

• The relationship between the input and output emf is given by the transformer equation.

22 1

1

induced emf in secondary =

number of turns in secondaryapplied emf in primary

number of turns in primary

NV V

N



Chapter 20

Transformers


http://lcmrschooldistrict.com/roth/Physics_animate/Ch20/3-transformers.swf




Chapter 20

Transformers, continued

• The transformer equation assumes that no power is lost between the primary and secondary coils. However, real transformers are not perfectly efficient.

• Real transformers typically have efficiencies ranging from 90% to 99%.

• The ignition coil in a gasoline engine is a transformer.



Chapter 20

A Step-Up Transformer in an Auto Ignition System





Chapter 20

Objectives

• Describe what electromagnetic waves are and how they are produced.

• Recognize that electricity and magnetism are two aspects of a single electromagnetic force.

• Explain how electromagnetic waves transfer energy.

• Describe various applications of electromagnetic waves.




Chapter 20

Propagation of Electromagnetic Waves

• Electromagnetic waves travel at the speed of light and are associated with oscillating, perpendicular electric and magnetic fields.

• Electromagnetic waves are transverse waves; that is, the direction of travel is perpendicular to the the direction of oscillating electric and magnetic fields.

• Electric and magnetic forces are aspects of a single force called the electromagnetic force.



Chapter 20

Electromagnetic Waves


http://lcmrschooldistrict.com/roth/Physics_animate/Ch20/4-em-waves.swf




Chapter 20

Propagation of Electromagnetic Waves, continued• All electromagnetic waves are produced by

accelerating charges.

• Electromagnetic waves transfer energy. The energy of electromagnetic waves is stored in the waves’ oscillating electric and magnetic fields.

• Electromagnetic radiation is the transfer of energy associated with an electric and magnetic field. Electromagnetic radiation varies periodically and travels at the speed of light.



Chapter 20

The Sun at Different Wavelengths of Radiation





Chapter 20

Propagation of Electromagnetic Waves, continued• High-energy electromagnetic waves behave like

particles.

• An electromagnetic wave’s frequency makes the wave behave more like a particle. This notion is called the wave-particle duality.

• A photon is a unit or quantum of light. Photons can be thought of as particles of electromagnetic radiation that have zero mass and carry one quantum of energy.




Chapter 20

The Electromagnetic Spectrum

• The electromagnetic spectrum ranges from very long radio waves to very short-wavelength gamma waves.

• The electromagnetic spectrum has a wide variety of applications and characteristics that cover a broad range of wavelengths and frequencies.




Chapter 20

The Electromagnetic Spectrum, continued

• Radio Waves– longest wavelengths– communications, tv

• Microwaves– 30 cm to 1 mm– radar, cell phones

• Infrared– 1 mm to 700 nm– heat, photography

• Visible light– 700 nm (red) to 400 nm (violet)

• Ultraviolet– 400 nm to 60 nm– disinfection, spectroscopy

• X rays– 60 nm to 10–4 nm– medicine, astronomy, security screening

• Gamma Rays– less than 0.1 nm– cancer treatment, astronomy



Chapter 20

The Electromagnetic Spectrum




Chapter 20

Ways of Inducing a Current in a Circuit


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