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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 :

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Chapter 23: Electromagnetic Waves

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  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

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