Chapter 34: Electromagnetic Waves

• Maxwell's equations: Four equations that contain all information on how electric and magnetic fields are produced,

∫_S E · dA = q_enc/ε₀   (Gauss' law for E, equivalent to Coulomb's law)
∫_C E · ds = – dΦ_B/dt   (Faraday's law)
∫_S B · dA = 0   (Gauss' law for B)
∫_C B · ds = μ₀I_enc + μ₀ε₀ dΦ_E/dt (Ampère-Maxwell law).

Relationship between the right-hand sides of the equations and the absence of magnetic monopoles.

• Displacement current: Can be seen in the second term of the right-hand side in the Ampère-Maxwell equation,

I_d = ε₀ dΦ_E/dt .

• Electromagnetic waves: Plane harmonic waves propagating along the x direction, for example, have

E = E_max cos(kx – ωt)  and  B = B_max cos(kx – ωt) ,

where k = 2/λ, ω = 2πf and, as for all waves, λf = v, the speed. The fields E and B are perpendicular to each other and to the direction of propagation, with E/B = c, and in vacuo the speed is

c = (μ₀ε₀)^–1/2 = 3.00 × 10⁸ m/s .

• Energy carried by electromagnetic waves: The Poynting vector S = (1/μ₀) E × B, representing the energy crossing a surface perpendicular to the direction of propagation, per unit area and unit time.
   
• Momentum and radiation pressure: The pressure exerted by radiation on a surface on which it is normally incident is P = S/c if the surface is absorbing and P = 2S/c if it is reflecting (S is the magnitude of the Poynting vector).
   
• Electromagnetic spectrum: It includes, in order of decreasing wavelength (increasing frequency) radio waves, infrared radiation, visible light, ultraviolet radiation, X-rays, gamma rays. Visible light corresponds to wavelengths approximately between 400 and 700 nm.