Maxwell equations andelectromagnetic waves

Gauss´s law

Induced fields

Analogy predicted by James Clark Maxwell

We know a similar equation :

Displacement current

→ A current and a changing electric fieldgive a magnetic field exactly in same form

Material equations: D = e e0 EB = µ µ0 Hj = s E

Electromagnetic spectrum

Electromagnetic radiation Kap 33 page 915

Wave equation ??

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

Wave propagates along x- direction

Faraday´s law

Flux FB through rectangle

Maxwell´s law

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

Polarization, Reflection andRefraction

Polarization

Reflection and refraction

n1

n2

Law of reflection

Law of refraction

Polarization by Reflection , Brewster´s law

Chromatic dispersion

Total internal reflection

Augustin Fresnel1788-1827

Fresnel's Equations for Reflection and Transmission

R + T = 1

Taken from: https://www.brown.edu/research/labs/mittleman/sites/brown.edu.research.labs.mittleman/files/uploads/lecture13_0.pdf