electromagnetism giancoli ch.21-29 physics of astronomy, winter week 7 review of waves and wave...
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![Page 1: 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](https://reader033.vdocuments.site/reader033/viewer/2022051415/56649d545503460f94a3056b/html5/thumbnails/1.jpg)
ElectromagnetismGiancoli 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 speed of light!• Magnetic monopole more symmetry
• Today: to American Physical Society meeting!• Next Friday 1:00-2:00 in 1050 Lab I: Science
Carnival poster session
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Waves
( , ) sin( )MD x t D kx t
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Wave equation
1. Differentiate D/t 2D/t2
2. Differentiate D/x 2D/x2
3. Find the speed from 22
222 2 22 2
2
2
2
Dt T f v
D k Tx
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Causes and effects of E
Gauss: E fields diverge from charges
Lorentz force: E fields can move charges
F = q E
0
AdEq
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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 I0ldB
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Changing fields create new fields!
Faraday: Changing magnetic flux induces circulating electric field
Guess what a changing E field induces?
lE ddt
d B
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Changing E field creates B field!
Current piles charge onto capacitor
Magnetic field doesn’t stop
Changing electric flux
“displacement current” magnetic circulation
lB ddt
d E
00AE dE
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Partial Maxwell’s equations
Charge E field Current B field
FaradayChanging B E
AmpereChanging E B
0
AdEq
I0ldB
lE ddt
d B lB d
dt
d E
00
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Maxwell eqns electromagnetic waves
Consider waves traveling in the x direction with frequency f=
and wavelength = /k
E(x,t)=E0 sin (kx-t) and
B(x,t)=B0 sin (kx-t)
Do these solve Faraday and Ampere’s laws?
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Faraday + Ampere
lE ddt
d B
dx
dB
dt
dE00
dx
dE
dt
dB
lB ddt
d E
00
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dx
dB
dt
dE00
dx
dE
dt
dB
Sub in: E=E0 sin (kx-t) and B=B0 sin (kx-t)
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Speed of Maxwellian waves?
Faraday: -B0 = k E0 Ampere: 00E0=kB0
Eliminate B0/E0 and solve for v=/k
0=xm = xC2 N/m2
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Maxwell equations Light
E(x,t)=E0 sin (kx-t) and B(x,t)=B0 sin (kx-t)solve Faraday’s and Ampere’s laws.
Electromagnetic waves in vacuum have speed c and energy/volume = 1/2 0 E2 = B2 /(20 )
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Full Maxwell equations
0
AdEq
B dA 0
Bdd
dt
E l
0 0 0Ed
d Idt
B l
Notice the asymmetries – how can we make these symmetric by adding a magnetic monopole?