1 / 20

Chapter 32

Chapter 32. Maxwell’s Equations. The electric field spreads into space proportional to the amount of static charge and how closely you space the static charges. Magnetic field lines are closed loops and always return to the source creating them.

kimberley-peck
Download Presentation

Chapter 32

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 32

  2. Maxwell’s Equations The electric field spreads into space proportional to the amount of static charge and how closely you space the static charges Magnetic field lines are closed loops and always return to the source creating them An electric field, resembling a magnetic field in shape, can be created by a time-varying magnetic field. There are two ways to produce a magnetic field: 1) by a current and 2) by a time-varying electric field.

  3. Maxwell’s Equations for Vacuum • In vacuum, there is no charge so renc=0 • Since no charge, no currents enclosed so J=0 • Note the symmetry of the equations i.e. they look practically the same!!

  4. Without proof

  5. Separating E from B

  6. The Wave Equation • This equation is called a wave equation. • In order to simplify the math, let’s just work with 1-dimension i.e. in the x-direction

  7. A solution is a sine function

  8. Using the wavelength and wave number fl is the speed of the wave, which we will call c

  9. An important revelation

  10. However, I could have solved for B

  11. Very similar functions • So the solution for E and B are mathematically similar • Now, let’s assign a direction for E in the y-direction

  12. Using the curl

  13. Implications • The wave is called transverse; both E and B are perpendicular to the propagation of the wave. The direction of propagation is in the direction of E x B. • E=cB • The wave travels in vacuum with a definite and unchanging speed • What is the wave propagating through?

  14. “Common Sense” on Waves • Ocean waves propagate in water • Sound waves propagate in air • Mechanical waves propagate through material where they are transmitting • Ergo, the 19th Century physicists thought that EM waves propagate through the “ether”. • Ether surrounds us and we move through it without any drag.

  15. Michelson-Morley Experiment • In 1887, Michelson and Morley invented an experiment to measure the speed of light in the direction of Earth’s motion and in the direction against Earth’s motion • If there is ether, then there should be a slight difference in the speed of light. • Michelson-Morley found NO evidence of any difference of the speed of light. • Why?

  16. The New Physics • Actually, if they trusted their equations, they would have seen that there is no need to have a medium

  17. A completely different direction • Einstein thought about the results of the MM experiment. • He assumed that there was no mistake and the c is always constant • The Postulates of Special Relativity • The laws of physics are the same in every inertial frame of reference • The speed of light in vacuum is the same in all inertial frames of reference and is independent of the motion of the source • This is the beginning of the new physics of the 20th century • From here, we can get E=mc2 and from there, quantum mechanics

  18. Waves in Matter • Recall e=ke0 • m=kmm0 • c=1/sqrt(m0e0) • Let v=speed of light in a material • v=1/sqrt(me) < c • v=c/sqrt(k*km) • Index of refraction, n • n=c/v=sqrt(k*km)

  19. Radiation Pattern • The Poynting Vector, S,describes the energy flow per unit area and per unit time through a cross-sectional area perpendicular to propagation direction • S=(E x B)/m0 • The “intensity” of the EM wave in vacuum is defined as • I=Sav=(E0B0)/2m0= ½ e0cE02

  20. EM Spectrum

More Related