Poynting Vector
S = (1/μ₀) E×B. Energy flow direction & intensity of EM wave.
Key Notes
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).
Formulas
Poynting vector (instantaneous)
Vector — points in propagation direction; magnitude oscillates with the wave.
Time-averaged intensity (plane wave)
Most-quoted form for intensity in W/m².
Alternative form
Intensity = speed × average energy density.
Intensity from a point source
Inverse-square law for isotropic radiator (e.g., a bulb).
Solar constant
Time-averaged solar power per unit area at Earth's orbit, before atmospheric absorption.
Important Points
Direction matters: S points where energy GOES, not where charges are. In a circuit, energy actually flows in the SPACE around the wires, not inside them.
For a sinusoidal wave, sin²(ωt) averages to ½ over a full cycle — that's where the factor of ½ in I = ½ε₀cE₀² comes from.
If you DOUBLE the field amplitude, intensity QUADRUPLES (I ∝ E₀²).
Solar constant ≈ 1361 W/m². After atmospheric absorption (~30%) and cosine angle losses, peak ground irradiance is ~1000 W/m² (sunny noon, equator).
For lasers, intensity can be enormous despite small total power — because the beam is narrow (small A).
u_avg = ½ε₀E₀² (averaged) — this is the energy density, NOT the peak.
Poynting Vector notes from sciphylab (also known as SciPhy, SciPhy Lab, SciPhy Labs, Physics Lab). Class 12 physics revision for JEE Mains, JEE Advanced, NEET UG, AP Physics 1/2/C, SAT, and CUET-UG.