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Electromagnetism PHYS20141
[email protected]
Schuster 4-11
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PHYS20141 Electromagnetism2
4. Electromagnetic waves
4.1 Wave equation & plane waves
4.2 Maxwell’s equations in free space
4.3 Poynting vector, intensity & radiation pressure
4.4 Polarization of EM waves
4.5 [Reflection of EM waves at a perfect conductor]
4.6 EM waves in the presence of a current
4.7 [EM waves in a dielectric and magnetic media]
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Week 10
- Wave equation in 1D
- Plane waves
- Maxwell’s equations in free space
- Wave equation for the E-field
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Solutions of the wave equation in 1D
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x
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Evolution of phase in 1D
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t
x2π-2π-4π
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3D Plane Waves
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Maxwell’s equations
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Maxwell’s equations in free space
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Electromagnetic waves
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“Light”…
+ Special Relativity (Einstein 1905)
1887,1888 (Hertz) 1895 (Roentgen)
1900 (Villard)
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Quotes…
JCM: I have also a paper afloat, containing an electromagnetic
theory of
light, which, till I am convinced to the contrary, I hold to be
great guns.
Einstein: The special theory of relativity owes its origins to
Maxwell's
equations of the electromagnetic field.
Steven Weinberg: [Nobel Prize 1979, Electroweak unification]
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PHYS20141 Electromagnetism13
JCM: I have also a paper afloat, containing an electromagnetic
theory of
light, which, till I am convinced to the contrary, I hold to be
great guns.
Einstein: The special theory of relativity owes its origins to
Maxwell's
equations of the electromagnetic field.
Steven Weinberg: If you have bought one of those T-shirts with
Maxwell’s
equations on the front, you may have to worry about its going
out of
style…
Quotes…
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PHYS20141 Electromagnetism14
JCM: I have also a paper afloat, containing an electromagnetic
theory of
light, which, till I am convinced to the contrary, I hold to be
great guns.
Einstein: The special theory of relativity owes its origins to
Maxwell's
equations of the electromagnetic field.
Steven Weinberg: If you have bought one of those T-shirts with
Maxwell’s
equations on the front, you may have to worry about its going
out of
style, but not about its becoming false. We will go on
teaching
Maxwellian electrodynamics as long as there are scientists.
Quotes…
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Going further…
- E, B and k perpendicular – general case
- Poynting vector(s)
- Intensity
- Radiation pressure
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Summary (and k!)
with ω = c|k| NB. |k| = wavenumber = 2π/λω = angular frequency =
2πf
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Helpful formulae
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Electromagnetic waves
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E
B
k
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Wave travelling through a box
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c∆t
∆A
Flux in Flux out
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Poynting vector (1)
� Microscopic definition
� Units
� Physical interpretation
- energy flux through a surface
- N is in the direction of wave motion
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Poynting vector (2)
� Macroscopic definition (materials)
N = E x H
� Units
� Physical interpretation
- energy flux through a surface
- N is in the direction of wave motion
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Radiation pressure
� Momentum of photon is p = U/c
At a boundary the radiation creates a force, Fr
� All radiation absorbed : Fr = A/c
� All radiation reflected : Fr = 2A/c
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