1 / 55

Chapter 23: Electromagnetic Waves

Chapter 23: Electromagnetic Waves. Chapter Outline. 1. Changing Magnetic Fields Produce Electric Fields. Faraday’s Law! (Ch. 21). Chapter Outline. 1. Changing Magnetic Fields Produce Electric Fields 2. Modification of Amp è re’s Law :

dkirby
Download Presentation

Chapter 23: Electromagnetic Waves

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Chapter 23: Electromagnetic Waves

  2. Chapter Outline • 1. Changing Magnetic Fields • Produce Electric Fields Faraday’s Law! (Ch. 21)

  3. Chapter Outline • 1. Changing Magnetic Fields • Produce Electric Fields • 2. Modification of Ampère’s Law: • Maxwell’s Displacement Current • (Changing Electric Fields Produce Magnetic Fields) Faraday’s Law! (Ch. 21)

  4. Chapter Outline • 1. Changing Magnetic Fields • Produce Electric Fields • 2. Modification of Ampère’s Law: • Maxwell’s Displacement Current • (Changing Electric Fields Produce Magnetic Fields) • 3. Gauss’s Law for Magnetic Fields • Magnetic “Charge” Doesn’t Exist! Faraday’s Law! (Ch. 21)

  5. Chapter Outline • 1. Changing Magnetic Fields • Produce Electric Fields • 2. Modification of Ampère’s Law: • Maxwell’s Displacement Current • (Changing Electric Fields Produce Magnetic Fields) • 3. Gauss’s Law for Magnetic Fields • Magnetic “Charge” Doesn’t Exist! • 4. Gauss’s Law for Electric Fields Faraday’s Law! (Ch. 21)

  6. Chapter Outline • 1. Changing Magnetic Fields • Produce Electric Fields • 2. Modification of Ampère’s Law: • Maxwell’s Displacement Current • (Changing Electric Fields Produce • Magnetic Fields) • 3. Gauss’s Law for Magnetic Fields • Magnetic “Charge” Doesn’t Exist! • 4. Gauss’s Law for Electric Fields Faraday’s Law! (Ch. 21) “Maxwell’s Equations”

  7. 1. Changing Electric Fields Produce • Magnetic Fields • 2. Modification of Ampère’s Law: • Maxwell’s Displacement Current • (Changing Electric Fields Produce • Magnetic Fields) • 3. Gauss’s Law for Magnetic Fields • 4. Gauss’s Law for Electric Fields “Maxwell’s Equations” • From these come production of • Electromagnetic Waves& their Speed • And Light is an Electromagnetic Wave!

  8. Derived from Maxwell’s Equations:

  9. Derived from Maxwell’s Equations: Light is an Electromagnetic Wave

  10. Derived from Maxwell’s Equations: Light is an Electromagnetic Wave The Electromagnetic Spectrum

  11. Derived from Maxwell’s Equations: Light is an Electromagnetic Wave The Electromagnetic Spectrum Measuring The Speed of Light

  12. Derived from Maxwell’s Equations: • Light is an Electromagnetic Wave • The Electromagnetic Spectrum • Measuring The Speed of Light • Energy & Momentum in • Electromagnetic Waves

  13. Derived from Maxwell’s Equations: • Light is an Electromagnetic Wave • The Electromagnetic Spectrum • Measuring The Speed of Light • Energy & Momentum in • Electromagnetic Waves • The Poynting Vector

  14. Derived from Maxwell’s Equations: • Light is an Electromagnetic Wave • The Electromagnetic Spectrum • Measuring The Speed of Light • Energy & Momentum in • Electromagnetic Waves • The Poynting Vector • Radiation Pressure

  15. Derived from Maxwell’s Equations: • Light is an Electromagnetic Wave • The Electromagnetic Spectrum • Measuring The Speed of Light • Energy & Momentum in • Electromagnetic Waves • The Poynting Vector • Radiation Pressure • Radio & Television

  16. Derived from Maxwell’s Equations: • Light is an Electromagnetic Wave • The Electromagnetic Spectrum • Measuring The Speed of Light • Energy & Momentum in • Electromagnetic Waves • The Poynting Vector • Radiation Pressure • Radio & Television • Wireless Communication

  17. Electromagnetic Theory • The theoretical understanding of electricity & magnetism seemed complete by around 1850: • Coulomb’s Law & Gauss’ Law explained electric fields & forces • Ampère’s Law & Faraday’s Law explained magnetic fields & forces • These laws were verified in many experiments

  18. Unanswered Questions (1850) • What is the nature of electric & magnetic fields? • What is the idea of action at a distance? • How fast do the field lines associated with a charge react to a movement in the charge? • James Clerk Maxwell studied some of these questions in the mid-1800’s • His work led to the discovery of electromagnetic waves

  19. Discovery of EM Waves • A time-varying magnetic field causes the creation of an electric field

  20. Discovery of EM Waves • A time-varying magnetic field causes the creation of an electric field • A magnetic field can produce an electric field

  21. Discovery of EM Waves • A time-varying magnetic field causes the creation of an electric field • A magnetic field can produce an electric field • Maxwell proposed a modification to Ampère’s Law such that a time-varying electric field produces a magnetic field

  22. Discovery of EM Waves • A time-varying magnetic field causes the creation of an electric field • A magnetic field can produce an electric field • Maxwell proposed a modification to Ampère’s Law such that a time-varying electric field produces a magnetic field • This gives a new way to create a magnetic field

  23. Discovery of EM Waves • A time-varying magnetic field causes the creation of an electric field • A magnetic field can produce an electric field • Maxwell proposed a modification to Ampère’s Law such that a time-varying electric field produces a magnetic field • This gives a new way to create a magnetic field • It also gives the equations of electromagnetism some symmetry

  24. Symmetry of E and B • The correct form of Ampère’s Law (due to Maxwell): A changing electric flux produces a magnetic field. • Since a changing electric flux can be caused by a changing E, this was an indication that a changing electric field produces a magnetic field

  25. Symmetry of E and B • Faraday’s Lawsays that a changing magnetic flux produces an induced emf, & an emf is always associated with an electric field • Since a changing magnetic flux can be caused by a changing B, we can also say that A changing magnetic field produces an electric field

  26. Symmetry of E and B

  27. Maxwell’s Ideas & Reasoning Consider Faraday’s Law:

  28. Maxwell’s Ideas & Reasoning • Consider Faraday’s Law: • A time dependent Magnetic Fieldinduces • an Electric Field.

  29. Maxwell’s Ideas & Reasoning • Consider Faraday’s Law: • A time dependent Magnetic Fieldinduces • an Electric Field. • Question: In an analogy with Faraday’s • Law, does a time dependent Electric Field • induce a Magnetic Field?

  30. Maxwell’s Ideas & Reasoning • Consider Faraday’s Law: • A time dependent Magnetic Fieldinduces • an Electric Field. • Question: In an analogy with Faraday’s • Law, does a time dependent Electric Field • induce a Magnetic Field? • The answer, based on experiment, is YES!!!

  31. Maxwell’s Ideas & Reasoning • Consider Faraday’s Law: • A time dependent Magnetic Fieldinduces • an Electric Field. • Question: In an analogy with Faraday’s • Law, does a time dependent Electric Field • induce a Magnetic Field? • The answer, based on experiment, is YES!!! • So, Ampère’s Lawneeds to be modifiedto • account for this!!!

  32. Maxwell’s Ideas & Reasoning • Consider Faraday’s Law: • A time dependent Magnetic Fieldinduces • an Electric Field. • Question: In an analogy with Faraday’s • Law, does a time dependent Electric Field • induce a Magnetic Field? • The answer, based on experiment, is YES!!! • So, Ampère’s Lawneeds to be modifiedto • account for this!!! • The modification is to add a time dependent • Electric Field to the right side ofAmpère’s Law

  33. Also: Consider Gauss’s Law:

  34. Also: Consider Gauss’s Law: • Applies to Electric Fields & is about the E field • produced by electric charges.

  35. Also: Consider Gauss’s Law: • Applies to Electric Fields & is about the E field • produced by electric charges. • Question: Is there an analogous Law for • Magnetic Fields?

  36. Also: Consider Gauss’s Law: • Applies to Electric Fields & is about the E field • produced by electric charges. • Question: Is there an analogous Law for • Magnetic Fields? • The answer, based on experiment, is YES!!!

  37. Also: Consider Gauss’s Law: • Applies to Electric Fields & is about the E field • produced by electric charges. • Question: Is there an analogous Law for • Magnetic Fields? • The answer, based on experiment, is YES!!! • However, experiments also show that there are • no “Magnetic Charges” (Magnetic Monopoles) • which are analogous to electric charges.

  38. Also: Consider Gauss’s Law: • Applies to Electric Fields & is about the E field • produced by electric charges. • Question: Is there an analogous Law for • Magnetic Fields? • The answer, based on experiment, is YES!!! • However, experiments also show that there are • no “Magnetic Charges (Magnetic Monopoles)” • which are analogous to electric charges. • So, Gauss’s Law for Magnetic Fields is • B = 0 For any CLOSED surface!

  39. Changing Electric Fields Produce Magnetic Fields: Ampère’s Law& Displacement CurrentMaxwell’s Generalization of Ampère’s Law • A wire is carrying current I. • RecallAmpère’s Law: • B(2r) = 0Iencl • for any closed loop • This relates the magnetic field B • around a current to the current Iencl • through a surface

  40. Changing Electric Fields Produce Magnetic Fields: Ampère’s Law& Displacement CurrentMaxwell’s Generalization of Ampère’s Law • Faraday’s Law: • “Theemf inducedin a • circuit is equal to the time • rate of changeof magnetic • flux through the circuit.” • So, changing Magnetic • Fieldsproduce currents • & thus Electric Fields

  41. Maxwell’sreasoning about Ampère’s Law: • For Ampere’s Lawto hold, it can’t • matter which surface is chosen. • But look at a discharging capacitor; • there is current through surface 1 • but there is none through surface 2:

  42. Maxwell’sreasoning about Ampère’s Law: • Therefore, Maxwell modified Ampère’s Law to include the creation of a magnetic field by a changing electric field. • This is analogous to Faraday’s Law which says that • electric fields can be produced by changing magnetic • fields. In the case shown, the electric field between • the plates of the capacitor is changing & so a magnetic • field must be produced between the plates.

  43. Maxwell’sreasoning about Ampère’s Law: • Results in a new version of Ampère’s Law: E B(2r) = B(2r) = B(2r) = B(2r) = B(2r) =

  44. Example: Charging A Capacitor. • A C = 30-pF air-gap capacitor has circular plates of • area A = 100 cm2. It is charged by a V = 70-V battery • through a R = 2.0-Ωresistor. At the instant the battery is • connected, the electric field between the plates is • changing most rapidly. At this instant, calculate • (a) The current into the plates, • and • (b) The rate of change of the E field between the plates. • (c) The B field induced between the plates. • Assume that E is uniform between the plates at • any instant & is zero at all points beyond the • edges of the plates.

  45. Capacitor with Circular Plates

  46. Solution: Circular Plate Capacitor • A C = 30-pF air-gap capacitor has circular plates of area A = 100 • cm2. Charged by a V0= 70-V battery through a R = 2.0-Ωresistor. • At the instant the battery is connected, the Efield between the • plates is changing most rapidly. At this instant, calculate • (a) The current into the plates. We know, for charge Q • on capacitor plates, time dependence is: • I = (Q/t). At t = 0, this must • be given by Ohm’s Law: I = (V0/R) = 35A

  47. Solution: Circular Plate Capacitor • A C = 30-pF air-gap capacitor has circular plates of area A = 100 • cm2. Charged by a V0= 70-V battery through a R = 2.0-Ωresistor. • At the instant the battery is connected, the Efield between the • plates is changing most rapidly. At this instant, calculate • (b) The rate of change of the E field between the plates. • The E field between two closely spaced conductors is: • E = /0 = Q(t)/(0A). So(E/t) = (Q/t)/(0A) at t = 0 • (E/t) = I/(0A) = 4  1014 V/(m s)

  48. Solution: Circular Plate Capacitor • A C = 30-pF air-gap capacitor has circular plates of area A = 100 • cm2. Charged by a V0= 70-V battery through a R = 2.0-Ωresistor. • At the instant the battery is connected, the Efield between the • plates is changing most rapidly. At this instant, calculate • (c) The B field induced between the plates. • Use Ampere’s Law with Displacement Current to solve this. • B(2πr) = 0μ0(E/t) = 0μ0(πr2)(E/t) • B = 0μ0(½)r (E/t) at outer radius r = 5.6 cm • B = 1.2  10-4 T

  49. The second term in Ampere’s Law, first • written by Maxwell, has the dimensions of • current (after factoring out μ0), & is sometimes • called the Displacement Current: B(2r) = B(2r) = B(2r) = E  where t

  50. Gauss’s Law for Magnetism • Gauss’s law relates the electric field on a • closed surface to the net charge enclosed by • that surface. The analogous law for • magnetic fields is different, as there are no • single magnetic point charges (monopoles): BA BA

More Related