Electromagnetic waves are transverse waves where electric field E and magnetic field B oscillate perpendicular to each other and to the direction of propagation. In vacuum, the wave speed is the speed of light c ≈ 3.00 × 10⁸ m/s, related to permittivity and permeability by c = 1/√(μ₀ ε₀). The Poynting vector S = (1/μ₀)(E × B) describes energy flow, with average intensity I = E₀² / (2 μ₀ c) = c B₀² / (2 μ₀). The full electromagnetic spectrum ranges from radio waves to gamma rays.
EM wave calculators
Speed, intensity, energy density, spectrum, displacement current and radiation pressure
📈 EM wave visualization
Basic properties of electromagnetic waves
| Concept | Formula / Value | Notes |
|---|---|---|
| Speed in vacuum | c = 3.00 × 10⁸ m/s | Exact: c = 299 792 458 m/s |
| Speed in medium | v = 1/√(μ ε) | c = 1/√(μ₀ ε₀) in vacuum |
| Relation between E and B | E = c B (vacuum) | E ⟂ B ⟂ direction |
| Plane EM wave | E = E₀ sin(kx − ωt + φ) | k = 2π/λ, ω = 2πf |
| Poynting vector | S = (1/μ₀)(E × B) | Direction of energy flow |
| Average intensity | I = E₀²/(2 μ₀ c) = c B₀²/(2 μ₀) | W/m² |
| Average energy density | u_avg = ε₀ E₀²/2 = B₀²/(2 μ₀) | Electric and magnetic parts equal |
EM spectrum and Maxwell’s correction
| Type / Concept | Range / Formula | Notes |
|---|---|---|
| Radio waves | λ > 1 m, f < 300 MHz | Communication (radio, TV, mobile) |
| Microwaves | 1 mm – 1 m | Radar, ovens, satellites |
| Infrared (IR) | 700 nm – 1 mm | Remote control, thermal imaging |
| Visible light | 400 – 700 nm | Human vision |
| Ultraviolet (UV) | 10 – 400 nm | Sterilization, tanning |
| X-rays | 0.01 – 10 nm | Medical imaging |
| Gamma rays | λ < 0.01 nm | Nuclear and cosmic sources |
| Displacement current density | J_d = ε₀ ∂E/∂t | Added by Maxwell |
| Ampere–Maxwell law | ∮ B·dl = μ₀ (I + I_d) | I_d = ε₀ dΦ_E/dt |
| Radiation pressure | P = I/c (absorb), 2I/c (reflect) | Force/area due to light |
About this electromagnetic waves tool
This page brings together the most important formulas for electromagnetic waves: speed in vacuum and media, relations between electric and magnetic fields, intensity and energy density, classification of the EM spectrum, Maxwell’s displacement current and radiation pressure. Use the calculators and step-by-step breakdowns to quickly solve textbook-style problems and build intuition for how E, B, c, I and u are connected.