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Electromagnetism and Energy

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Electromagnetism Giancoli Ch.21-29 Physics of Astronomy, winter week 7 Review of waves and wave equations Summary of EM & Maxwell s eqns Derive EM wave equation and ... – PowerPoint PPT presentation

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Title: Electromagnetism and Energy


1
ElectromagnetismGiancoli Ch.21-29Physics of
Astronomy, winter week 7
  • Review of waves and wave equations
  • Summary of EM Maxwells eqns
  • Derive EM wave equation and speed of light!
  • Magnetic monopole ? more symmetry
  • Today to American Physical Society meeting!
  • Next Friday 100-200 in 1050 Lab I Science
    Carnival poster session

2
Waves
3
Wave equation
1. Differentiate dD/dt ? d2D/dt2 2. Differentiate
dD/dx ? d2D/dx2 3. Find the speed from
4
Causes and effects of E
  • Gauss E fields diverge from charges
  • Lorentz force E fields can move charges
  • F q E

5
Causes and effects of B
  • Ampere B fields curl around currents
  • Lorentz force B fields can bend moving charges
  • F q v x B IL x B

6
Changing fields create new fields!
  • Faraday Changing magnetic flux induces
    circulating electric field
  • Guess what a changing E field induces?

7
Changing E field creates B field!
  • Current piles charge onto capacitor
  • Magnetic field doesnt stop
  • Changing electric flux
  • displacement current
  • magnetic circulation

8
Partial Maxwells equations
9
Maxwell eqns ? electromagnetic waves
  • Consider waves traveling in the x direction with
    frequency f w/2p
  • and wavelength l 2p/k
  • E(x,t)E0 sin (kx-wt) and
  • B(x,t)B0 sin (kx-wt)
  • Do these solve Faraday and Amperes laws?

10
Faraday Ampere
11
Sub in EE0 sin (kx-wt) and BB0 sin (kx-wt)
12
Speed of Maxwellian waves?
Faraday -wB0 k E0 Ampere
m0e0wE0kB0 Eliminate B0/E0 and solve for vw/k
e0 8.85 x 10-12 C2 N/m2
m0 4 p x 10-7 Tm/A
13
Maxwell equations ? Light
E(x,t)E0 sin (kx-wt) and B(x,t)B0 sin
(kx-wt) solve Faradays and Amperes
laws. Electromagnetic waves in vacuum have speed
c and energy/volume 1/2 e0 E2 B2 /(2m0 )
14
Full Maxwell equations
Notice the asymmetries how can we make these
symmetric by adding a magnetic monopole?
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