nhood
Uploaded by
23 SLIDES
255 VUES
230LIKES

Maxwell's Equations: Laws of Electromagnetism and Electromagnetic Waves

DESCRIPTION

Dive into Maxwell’s Equations, Gauss’ Laws, Faraday’s Law, Ampere’s Law, and electromagnetic waves in the electromagnetic spectrum. Explore displacement current and electromagnetic radiation phenomena.

1 / 23

Télécharger la présentation

Maxwell's Equations: Laws of Electromagnetism and 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 34 The Laws of Electromagnetism Maxwell’s Equations Displacement Current Electromagnetic Radiation

  2. The Electromagnetic Spectrum infra -red ultra -violet Radio waves g-rays m-wave x-rays

  3. The Equations of Electromagnetism (at this point …) Gauss’ Law for Electrostatics Gauss’ Law for Magnetism Faraday’s Law of Induction Ampere’s Law

  4. The Equations of Electromagnetism ..monopole.. Gauss’s Laws 1 ? 2 ...there’s no magnetic monopole....!!

  5. The Equations of Electromagnetism .. if you change a magnetic field you induce an electric field......... Faraday’s Law 3 Ampere’s Law 4 .......is the reverse true..?

  6. E B ...lets take a look at charge flowing into a capacitor... ...when we derived Ampere’s Law we assumed constant current...

  7. E B ...lets take a look at charge flowing into a capacitor... ...when we derived Ampere’s Law we assumed constant current... E B .. if the loop encloses one plate of the capacitor..there is a problem … I = 0 Side view:(Surface is now like a bag:)

  8. E B Maxwell solved this problem by realizing that.... Inside the capacitor there must be an induced magnetic field... How?.

  9. E B x x x x x x x x x x x x Maxwell solved this problem by realizing that.... Inside the capacitor there must be an induced magnetic field... How?. Inside the capacitor there is a changing E  B A changing electric field induces a magnetic field E

  10. E B x x x x x x x x x x x x Maxwell solved this problem by realizing that.... Inside the capacitor there must be an induced magnetic field... How?. Inside the capacitor there is a changing E  B A changing electric field induces a magnetic field E where Id is called the displacement current

  11. E B x x x x x x x x x x x x Maxwell solved this problem by realizing that.... Inside the capacitor there must be an induced magnetic field... How?. Inside the capacitor there is a changing E  B A changing electric field induces a magnetic field E where Id is called the displacement current Therefore, Maxwell’s revision of Ampere’s Law becomes....

  12. Derivation of Displacement Current For a capacitor, and . Now, the electric flux is given by EA, so: , where this current , not being associated with charges, is called the “Displacement current”, Id. Hence: and:

  13. Derivation of Displacement Current For a capacitor, and . Now, the electric flux is given by EA, so: , where this current, not being associated with charges, is called the “Displacement Current”, Id. Hence: and:

  14. Maxwell’s Equations of Electromagnetism Gauss’ Law for Electrostatics Gauss’ Law for Magnetism Faraday’s Law of Induction Ampere’s Law

  15. Maxwell’s Equations of Electromagnetismin Vacuum (no charges, no masses) Consider these equations in a vacuum..... ......no mass, no charges. no currents.....

  16. Maxwell’s Equations of Electromagnetismin Vacuum (no charges, no masses)

  17. Faraday’s law: dB/dt electric field Maxwell’s modification of Ampere’s law dE/dt magnetic field ˆ j ˆ z E(x, t) = EP sin (kx-t) B(x, t) = BP sin (kx-t) Electromagnetic Waves These two equations can be solved simultaneously. The result is:

  18. Electromagnetic Waves B E

  19. Electromagnetic Waves B E Special case..PLANE WAVES... satisfy the wave equation Maxwell’s Solution

  20. E(x, t) = EP sin (kx-t) B(x, t) = BP sin (kx-t) ˆ j ˆ z Plane Electromagnetic Waves Ey Bz c x

  21. F(x) x  F(x) v x Static wave F(x) = FP sin (kx + ) k = 2   k = wavenumber  = wavelength Moving wave F(x, t) = FP sin (kx - t)  = 2  f  = angular frequency f = frequency v =  / k

  22. F v Moving wave F(x, t) = FP sin (kx - t) x What happens at x = 0 as a function of time? F(0, t) = FP sin (-t) For x = 0 and t = 0  F(0, 0) = FP sin (0) For x = 0 and t = t  F (0, t) = FP sin (0 – t) = FP sin (– t) This is equivalent to: kx = - t  x = - (/k) t F(x=0) at time t is the same as F[x=-(/k)t] at time 0 The wave moves to the right with speed /k

  23. E(x, t) = EP sin (kx-t) B(x, t) = BP sin (kx-t) ˆ j ˆ z Plane Electromagnetic Waves Ey Bz Notes: Waves are in Phase, but fields oriented at 900. k=2p/l. Speed of wave is c=w/k (= fl) At all times E=cB. c x

More Related