Mastering EM Waves: Poynting Vector & Energy Density Guide

APEX CLASS • IITJEE Electromagnetic Waves Lab (Guaranteed 4 Marks)

EM Wave Vectors (E × B), Energy Density & Complete EM Spectrum

Master Poynting Vector Direction (E × B), 50:50 Energy Density Split, Displacement Current, and NCERT Spectrum Uses!

⚡ 1. EM Wave Vectors (E × B), Energy & Maxwell’s Law 🌈 2. Complete 7-Band Electromagnetic Spectrum Explorer

🔬 Select an EM Wave Property to Inspect 3D Vectors & Equations:

1. 3D Wave (E ⊥ B ⊥ c & In-Phase!) 2. Energy Density (u_E = u_B Split) 3. Displacement Current (I_d = I_c) 4. Radiation Pressure (I/c vs 2I/c)

Field Amplitude Ratio

E₀ = c · B₀ (k · E₀ = ω · B₀)

c = 3 × 10⁸ m/s in Vacuum

Energy Density Split

u_E = u_B = ¼ ε₀ E₀²

Total u = ½ ε₀ E₀² = B₀²/(2μ₀)

Wave Intensity (I)

I = ½ ε₀ E₀² c = P / A

Also I = (E_rms × B_rms) / μ₀

Radiation Force (F)

Abs: P/c | Mirror: 2P/c

Where P = I · A is Incident Power

🌈 Mnemonic: “Roman Men Invented Very Unusual X-Ray Guns” (λ Decreases →, Frequency f Increases →):

1. Radio & Microwaves (Longest λ) 2. Infrared & Visible Light 3. Ultraviolet (UV) & X-Rays 4. Gamma Rays (Highest Energy 🏆)

Longest Wavelength (λ)

Radio Waves (> 0.1 m)

Lowest Photon Energy E = hf

Shortest Wavelength (λ)

Gamma Rays (< 10⁻¹² m)

Highest Photon Energy (MeV)

Speed in Vacuum

v_radio = v_gamma = c

Ratio of Speeds in Vacuum = 1 : 1!

Wave Number (k)

k = 2π / λ = ω / c

From E = E₀ sin(ωt – kx)