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Chapter 29 Maxwell’s Equations and Electromagnetic Waves

Chapter 29 Maxwell’s Equations and Electromagnetic Waves. Oersted Denmark. Ampere France. Lenz Russia. Faraday England. Maxwell Scotland. Coulomb France.

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Chapter 29 Maxwell’s Equations and Electromagnetic Waves

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  1. Chapter 29 Maxwell’s Equations and Electromagnetic Waves

  2. Oersted Denmark Ampere France Lenz Russia Faraday England Maxwell Scotland Coulomb France All electric and magnetic phenomena could be described using only 4 equations involving electric and magnetic fields —— Maxwell’s equations → Culmination: Electromagnetic waves 2

  3. S2 S1 I Changing E produces B Changing magnetic field electric field Changing electric field magnetic field ? A beautiful symmetry in nature: Ampere’s law: ? 3

  4. S2 S1 + + + + I An extra term in Ampere’s law → changing E - - - - Discontinuity of current Ampere’s law: Contradiction? → discontinuity of the current Which result is right? 4

  5. S2 S1 + + + + I E - - - - Displacement current Conduction current: Electric field between plates: Displacement current: 5

  6. I Generalized Ampere’s law Ampere’s law in a general form: 1) ID is produced by changing electric field 2) Continuity of total current: 6

  7. Example1: A parallel-plate capacitor is charging with . Determine (a) the conduction current I; (b) magnetic field. I 0.1m Charging capacitor Solution: (a) Continuity of total current: 7

  8. r I 0.1m (b) magnetic field ? Generalized Ampere’s law: 8

  9. Question: The voltage on a capacitor is changing as . What is the EMF on the square coil inside the capacitor? d a a Capacitor in LC circuit 9

  10. Summary of electromagnetism Electrostatic / induced electric / total electricfield: Magneticfield created by IC or ID : 10

  11. Maxwell’s equations (1) Finally we can state all 4 of Maxwell’s equations: ① source of E ② no magnetic charges/monopoles ③ changing B → E ④ changing E → B 11

  12. Maxwell’s equations (2) Differential form of Maxwell’s equations: 1) Basic equations for all electromagnetism 2) As fundamental as Newton’s laws 3) Important outcome: electromagnetic waves 12

  13. Production of EM waves Maxwell’s prediction Hertz’s experiment “Antenna” Near field &radiation field → electromagnetic wave Also by accelerating charges 13

  14. Wave equations for EM wave Free space: no charges or conduction currents Wave equation! 14

  15. Speed of EM wave 3-D wave equation → 1-D (plane) wave equation Compare with standard wave equation: 15

  16. Properties of EM wave Particular solutions: 1) Transverse wave 2) In phase: 3) 16

  17. Energy in EM wave Total energy stored per unit volume in EM wave: Energy transports per unit time per unit area: 17

  18. Poynting vector Consider the direction of energy transporting: → Poynting vector Time averaged S is intensity: Example 2: Show the direction of energy transporting inside the battery and resistor. 18

  19. Sunshine Example3: Radiation from the Sun reaches the Earth at a rate about 1350W/m2. Assume it is a single EM wave, calculate E0 and B0. Solution: Rate→ time averaged S / intensity 19

  20. *Radiation pressure EM waves carry energy → also carry momentum Be absorbed / reflected →radiation pressure Absorbed: Reflected: 20

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