Maxwell equations and electromagnetic waves€¦ · electromagnetic waves. Gauss´s law Induced...
Transcript of Maxwell equations and electromagnetic waves€¦ · electromagnetic waves. Gauss´s law Induced...
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Maxwell equations andelectromagnetic waves
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Gauss´s law
Induced fields
Analogy predicted by James Clark Maxwell
We know a similar equation :
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Displacement current
→ A current and a changing electric fieldgive a magnetic field exactly in same form
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Material equations: D = e e0 EB = µ µ0 Hj = s E
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Electromagnetic spectrum
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Electromagnetic radiation Kap 33 page 915
Wave equation ??
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Wave equation
Ansatz : y= ym sin (wt - kx) E=E0 exp (i(wt-kx)
dy/dt = w ym sin (wt - kx)d²y/dt² = -w² ym sin (wt - kx)dy/dx = k ym sin (wt - kx)d²y/dx² = -k² ym sin (wt - kx)
-w² ym sin (wt - kx) = 1/v² (-k² ym sin (wt - kx))-w² = 1/v² (-k²)
v = l f
c = 299 792 458 m/sSpeed of light
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Wave propagates along x- direction
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Faraday´s law
Flux FB through rectangle
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Maxwell´s law
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Energy transport
Right hand rule
E and B are perpendicular to each other
B=E/c
intensity
Root mean square value of E Dependence on distance
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Polarization, Reflection andRefraction
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Polarization
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Reflection and refraction
n1
n2
Law of reflection
Law of refraction
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Polarization by Reflection , Brewster´s law
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Chromatic dispersion
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Total internal reflection
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Augustin Fresnel1788-1827
Fresnel's Equations for Reflection and Transmission
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R + T = 1
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Taken from: https://www.brown.edu/research/labs/mittleman/sites/brown.edu.research.labs.mittleman/files/uploads/lecture13_0.pdf