Chapter 35. Electromagnetic Fields and Waves

1. 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.

2. Chapter 35. Electromagnetic Fields and Waves 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

3. Chapter 35. Reading Quizzes

4. Maxwell’s equations are a set of how many equations? • Two • Three • Four • Five • Six

5. Maxwell’s equations are a set of how many equations? • Two • Three • Four • Five • Six

6. Maxwell introduced the displacement current as a correction to • Coulomb’s law. • Gauss’s law. • Biot-Savart’s law. • Ampère’s law. • Faraday’s law.

7. Maxwell introduced the displacement current as a correction to • Coulomb’s law. • Gauss’s law. • Biot-Savart’s law. • Ampère’s law. • Faraday’s law.

8. The law that characterizes polarizers is called • Malus’s law. • Maxwell’s law. • Poynting’s law. • Lorentz’s law.

9. The law that characterizes polarizers is called • Malus’s law. • Maxwell’s law. • Poynting’s law. • Lorentz’s law.

10. Experimenter A creates a magnetic field in the laboratory. Experimenter B moves relative to A. Experimenter B sees • just the same magnetic field. • a magnetic field of different strength. • a magnetic field pointing the opposite direction. • just an electric field. • both a magnetic and an electric field.

11. Experimenter A creates a magnetic field in the laboratory. Experimenter B moves relative to A. Experimenter B sees • just the same magnetic field. • a magnetic field of different strength. • a magnetic field pointing the opposite direction. • just an electric field. • both a magnetic and an electric field.

12. Chapter 35. Basic Content and Examples

13. E or B? It Depends on Your Perspective

14. 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.

15. 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.

16. Ampère’s law Whenever total current Ithrough 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, Ithrough = I1−I2 .

17. Tactics: Determining the signs of flux and current

18. 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

19. EXAMPLE 35.3 The fields inside a charging capacitor QUESTION:

20. EXAMPLE 35.3 The fields inside a charging capacitor

21. EXAMPLE 35.3 The fields inside a charging capacitor

22. EXAMPLE 35.3 The fields inside a charging capacitor

23. EXAMPLE 35.3 The fields inside a charging capacitor

24. Maxwell’s Equations

25. The Fundamental Ideas of Electromagnetism

26. 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.

28. Properties of Electromagnetic Waves Any electromagnetic wave must satisfy four basic conditions: • The fields Eand B and are perpendicular to the direction of propagation vem.Thus an electromagnetic wave is a transverse wave. • Eand B are perpendicular to each other in a manner such that E× Bis in the direction of vem. •  The wave travels in vacuum at speed vem = c • E = cBat any point on the wave.

29. Properties of Electromagnetic Waves The energy flow of an electromagnetic wave is described by the Poynting vector defined as The magnitude of the Poynting vector is The intensity of an electromagnetic wave whose electric field amplitude is E0 is

30. EXAMPLE 35.4 The electric field of a laser beam QUESTION:

31. EXAMPLE 35.4 The electric field of a laser beam

32. EXAMPLE 35.4 The electric field of a laser beam

33. EXAMPLE 35.4 The electric field of a laser beam

34. 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 prad.The radiation pressure on an object that absorbs all the light is where I is the intensity of the light wave. The subscript on prad is important in this context to distinguish the radiation pressure from the momentum p.

35. EXAMPLE 35.5 Solar sailing QUESTION:

36. EXAMPLE 35.5 Solar sailing

37. EXAMPLE 35.5 Solar sailing

38. EXAMPLE 35.5 Solar sailing

41. Malus’s Law Suppose a polarized light wave of intensity I0 approaches a polarizing filter. θis 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%.

42. Chapter 35. Summary Slides

43. General Principles

44. General Principles

45. General Principles

46. Important Concepts

47. Important Concepts

48. Applications

49. Chapter 35. Clicker Questions

50. Which diagram shows the fields in frame S´?