5. Waves and energy density

Question 1

What is the free polarisation/current density without any charges?

Answer 1

ρ_f=0
J_f=0

Question 2

What is the equation for phase velocity in a material?

Answer 2

v_φ=c/sqrt(µ_rε_r)=c/n

Question 3

What is the equation for refractive index?

Answer 3

n=sqrt(µ_rε_r)

Question 4

What is the common relative permeability for transparent matter?

Answer 4

µ_r~1

Question 5

What are Maxwell’s equations for matter in wave form?

Answer 5

k · D = 0
k · B = 0
k × E = ωB
k × H = −ωD

Question 6

What is the equation for impedance of free space?

Answer 6

Z₀ = µ₀c =sqrt(µ₀/ε₀)=376.73 Ω

Question 7

What is the impedance?

Answer 7

The relation of E and H for linear isotropic materia
Z=E/H

Question 8

What is the equation for the impedance of a material?

Answer 8

Z=µ_r/n Z₀
µ_r is typically ~1

Question 9

What is the Poynting vector for an electromagnetic field?

Answer 9

S = E × H

Question 10

What is the energy density for an electromagnetic field?

Answer 10

u =1/2 (E · D) + 1/2 (H · B)

Question 11

What is the magnitude of the Poynting vector for an electromagnetic field?

Answer 11

S=EH=E²/Z=ZH²

Question 12

What is the equation for the RMS amplitude?

Answer 12

E_RMS=E₀/sqrt(2)

Question 13

What is the relativistic energy of a photon?

Answer 13

E=pc

Question 14

What is the momentum flux for photons?

Answer 14

p=S/c= (E × H) /c

Question 15

What is the momentum density for photons?

Answer 15

p=S/c² = (E × H) /c²

Question 16

What is the magnetic field strength for a cylinder?

Answer 16

H= I/2πa

Question 17

What is the electric field strength for a cylinder?

Answer 17

E=V/L