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Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. Chapter 35. Electromagnetic Fields and Waves To understand a laser beam, we need to know how electric and magnetic fields change with time. Examples of time- dependent electromagnetic phenomena include high- speed circuits, transmission lines, radar, and optical communications. Chapter Goal: To study the properties of electromagnetic fields and waves.

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Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. Topics: E or B? It Depends on Your Perspective The Field Laws Thus Far The Displacement Current Maxwell’s Equations Electromagnetic Waves Properties of Electromagnetic Waves Polarization Chapter 35. Electromagnetic Fields and Waves

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Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. Chapter 35. Reading Quizzes

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Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. Maxwell’s equations are a set of how many equations? A.Two B.Three C.Four D.Five E.Six

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Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. Maxwell’s equations are a set of how many equations? A.Two B.Three C.Four D.Five E.Six

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Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. Maxwell introduced the displacement current as a correction to A.Coulomb’s law. B.Gauss’s law. C.Biot-Savart’s law. D.Ampère’s law. E.Faraday’s law.

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Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. Maxwell introduced the displacement current as a correction to A.Coulomb’s law. B.Gauss’s law. C.Biot-Savart’s law. D.Ampère’s law. E.Faraday’s law.

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Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. The law that characterizes polarizers is called A.Malus’s law. B.Maxwell’s law. C.Poynting’s law. D.Lorentz’s law.

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Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. The law that characterizes polarizers is called A.Malus’s law. B.Maxwell’s law. C.Poynting’s law. D.Lorentz’s law.

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Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. Experimenter A creates a magnetic field in the laboratory. Experimenter B moves relative to A. Experimenter B sees A.just the same magnetic field. B.a magnetic field of different strength. C.a magnetic field pointing the opposite direction. D.just an electric field. E.both a magnetic and an electric field.

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Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. Experimenter A creates a magnetic field in the laboratory. Experimenter B moves relative to A. Experimenter B sees A.just the same magnetic field. B.a magnetic field of different strength. C.a magnetic field pointing the opposite direction. D.just an electric field. E.both a magnetic and an electric field.

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Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. Chapter 35. Basic Content and Examples

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Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. E or B? It Depends on Your Perspective

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Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. E or B? It Depends on Your Perspective Whether a field is seen as “electric” or “magnetic” depends on the motion of the reference frame relative to the sources of the field.

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Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. E or B? It Depends on Your Perspective The Galilean field transformation equations are where V is the velocity of frame S' relative to frame S and where the fields are measured at the same point in space by experimenters at rest in each reference frame. NOTE: These equations are only valid if V << c.

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Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. Ampère’s law Whenever total current I through passes through an area bounded by a closed curve, the line integral of the magnetic field around the curve is The figure illustrates the geometry of Ampère’s law. In this case, I through = I 1 − I 2.

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Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. Tactics: Determining the signs of flux and current

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Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. The Displacement Current The electric flux due to a constant electric field E perpendicular to a surface area A is The displacement current is defined as Maxwell modified Ampère’s law to read

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Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. EXAMPLE 35.3 The fields inside a charging capacitor QUESTION:

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Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. EXAMPLE 35.3 The fields inside a charging capacitor

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Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. EXAMPLE 35.3 The fields inside a charging capacitor

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Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. EXAMPLE 35.3 The fields inside a charging capacitor

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Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. EXAMPLE 35.3 The fields inside a charging capacitor

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Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. Maxwell’s Equations

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Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. The Fundamental Ideas of Electromagnetism

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Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. Electromagnetic Waves Maxwell, using his equations of the electromagnetic field, was the first to understand that light is an oscillation of the electromagnetic field. Maxwell was able to predict that Electromagnetic waves can exist at any frequency, not just at the frequencies of visible light. This prediction was the harbinger of radio waves. All electromagnetic waves travel in a vacuum with the same speed, a speed that we now call the speed of light.

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Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley.

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Properties of Electromagnetic Waves 1.The fields E and B and are perpendicular to the direction of propagation v em.Thus an electromagnetic wave is a transverse wave. 2. E and B are perpendicular to each other in a manner such that E × B is in the direction of v em. 3. The wave travels in vacuum at speed v em = c 4. E = cB at any point on the wave. Any electromagnetic wave must satisfy four basic conditions:

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Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. The energy flow of an electromagnetic wave is described by the Poynting vector defined as The magnitude of the Poynting vector is Properties of Electromagnetic Waves The intensity of an electromagnetic wave whose electric field amplitude is E 0 is

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Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. EXAMPLE 35.4 The electric field of a laser beam QUESTION:

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Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. EXAMPLE 35.4 The electric field of a laser beam

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Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. EXAMPLE 35.4 The electric field of a laser beam

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Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. EXAMPLE 35.4 The electric field of a laser beam

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Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. Radiation Pressure It’s interesting to consider the force of an electromagnetic wave exerted on an object per unit area, which is called the radiation pressure p rad. The radiation pressure on an object that absorbs all the light is where I is the intensity of the light wave. The subscript on p rad is important in this context to distinguish the radiation pressure from the momentum p.

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Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. EXAMPLE 35.5 Solar sailing QUESTION:

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Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. EXAMPLE 35.5 Solar sailing

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Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. EXAMPLE 35.5 Solar sailing

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Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. EXAMPLE 35.5 Solar sailing

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Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley.

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Malus’s Law Suppose a polarized light wave of intensity I 0 approaches a polarizing filter. θ is the angle between the incident plane of polarization and the polarizer axis. The transmitted intensity is given by Malus’s Law: If the light incident on a polarizing filter is unpolarized, the transmitted intensity is In other words, a polarizing filter passes 50% of unpolarized light and blocks 50%.

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Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. Chapter 35. Summary Slides

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Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. General Principles

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Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. General Principles

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Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. General Principles

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Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. Important Concepts

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Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. Important Concepts

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Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. Applications

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Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. Chapter 35. Clicker Questions

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Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. Which diagram shows the fields in frame S´?

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Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. Which diagram shows the fields in frame S´?

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Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. The electric field in four identical capacitors is shown as a function of time. Rank in order, from largest to smallest, the magnetic field strength at the outer edge of the capacitor at time T. A. B a = B b > B c = B d B. B d > B c > B a = B b C. B a > B b > B c > B d D. B a = B a > B c > B d E. B c > B a > B d > B b

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Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. A. B a = B b > B c = B d B. B d > B c > B a = B b C. B a > B b > B c > B d D. B a = B a > B c > B d E. B c > B a > B d > B b The electric field in four identical capacitors is shown as a function of time. Rank in order, from largest to smallest, the magnetic field strength at the outer edge of the capacitor at time T.

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Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. An electromagnetic wave is propagating in the positive x-direction. At this instant of time, what is the direction of at the center of the rectangle? A.In the positive x-direction B.In the negative x-direction C.In the positive z-direction D.In the negative z-direction E.In the positive y-direction

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Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. A.In the positive x-direction B.In the negative x-direction C.In the positive z-direction D.In the negative z-direction E.In the positive y-direction An electromagnetic wave is propagating in the positive x-direction. At this instant of time, what is the direction of at the center of the rectangle?

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Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. An electromagnetic wave is traveling in the positive y-direction. The electric field at one instant of time is shown at one position. The magnetic field at this position points A.In the positive y-direction. B.In the negative y-direction. C.In the positive x-direction. D.In the negative x-direction. E.Away from the origin.

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Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. A.In the positive y-direction. B.In the negative y-direction. C.In the positive x-direction. D.In the negative x-direction. E.Away from the origin. An electromagnetic wave is traveling in the positive y-direction. The electric field at one instant of time is shown at one position. The magnetic field at this position points

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Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. The amplitude of the oscillating electric field at your cell phone is 4.0 µV/m when you are 10 km east of the broadcast antenna. What is the electric field amplitude when you are 20 km east of the antenna? A.4.0 µV/m B.2.0 µV/m C.1.0 µV/m D.There’s not enough information to tell.

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Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. A.4.0 µV/m B.2.0 µV/m C.1.0 µV/m D.There’s not enough information to tell. The amplitude of the oscillating electric field at your cell phone is 4.0 µV/m when you are 10 km east of the broadcast antenna. What is the electric field amplitude when you are 20 km east of the antenna?

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Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. A. I a = I d > I b = I c B. I b = I c > I a = I d C. I d > I a > I b = I c D. I b = I c > I a > I d E. I d > I a > I b > I c Unpolarized light of equal intensity is incident on four pairs of polarizing filters. Rank in order, from largest to smallest, the intensities I a to I d transmitted through the second polarizer of each pair.

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Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. A. I a = I d > I b = I c B. I b = I c > I a = I d C. I d > I a > I b = I c D. I b = I c > I a > I d E. I d > I a > I b > I c Unpolarized light of equal intensity is incident on four pairs of polarizing filters. Rank in order, from largest to smallest, the intensities I a to I d transmitted through the second polarizer of each pair.

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