Poynting Vector

The Poynting vector S = (1/μ₀)·(E × B) gives the instantaneous power per unit area carried by an EM wave, in the direction of propagation.

Units: W/m². It is the rate at which EM energy flows through a unit area perpendicular to S.

For a plane wave with E and B in phase: S = (1/μ₀)·E·B and S oscillates as sin²(ωt), always non-negative.

Average intensity ⟨S⟩ = I = ½ε₀cE₀² = E_rms B_rms/μ₀ = c·u_avg, where u_avg is the time-averaged energy density.

Energy density splits equally between E-field and B-field: u_E = u_B = ½ε₀E²(t) at every instant.

Intensity of a point source falls as 1/r² because the same power spreads over a sphere of area 4πr².

S is intimately tied to radiation pressure: P = I/c (absorber) or 2I/c (perfect reflector).