C34 - Electromagnetic Waves

Wave equation (EM)

Gauss’s Law (electric)

Gauss’s Law (magnetic)

Faraday’s Law

Ampere’s Law

displacement current

• consequence of an added magnetic field component due to changing electric flux

Lorentz force law

electromagnetic wave equation

• E & B are interchangeable

EM wave speed

E & B wave equations (terms of x & t)

E: j

B: k

E & B magnitude equations

• E_max/B_max = E/B = c

• B = ε₀μ₀cE

u_avg (average energy density)

• u = I/c

Poynting vector

• direction and magnitude of power per unit area of EM wave

EM speed in matter

v = 1/(εμ)^1/2 = 1/((KK_m)(ε₀μ₀))^1/2 = c/(KK_m)^1/2

• K = dielectric constant = ε/ε₀

• K_m = relative permeability = μ/μ₀

EM wave intensity

• remember energy density u for E & B!

flow rate of EM momentum

(1/A)(dp/dt) = S/c

Standing EM waves

• Eqn:

  • E_y = -2E_maxsin(kx)sin(ωt)

  • B_z = -2E_maxcos(kx)cos(ωt)

• Nodes:

  • x_E = nλ/2 (n = 0, 1, 2, 3, …)

  • x_B = nλ/4 (n = 1, 3, 5, …)

• Wavelength:

  • λ_n = 2L/n

  • f_n = c/λ_n = nc/2L