EM Wave Energy Calculator
Enter electric/magnetic field of an electromagnetic wave to compute energy densities and the Poynting vector (intensity).
Input Data
Results
At a glance:An electromagnetic wave carries energy in oscillating electric and magnetic fields. The electric energy density is u_E = ½ε₀E² and magnetic u_B = B²/(2μ₀); in a plane wave u_E = u_B, so total u = ε₀E² = B²/μ₀. The energy flux (intensity) is the Poynting vector S = E×B/μ₀, whose magnitude is I = E·B/μ₀ = E²/(μ₀c) = c·u. Time-averaged intensity for sinusoidal fields uses RMS values: ⟨S⟩ = E_rms·B_rms/μ₀. Here ε₀ ≈ 8.854×10⁻¹² F/m, μ₀ = 4π×10⁻⁷ H/m, c = 1/√(ε₀μ₀) ≈ 3×10⁸ m/s.
Formula
u_E = ½ε₀E²
u_B = B²/(2μ₀)
Total u = ε₀E² = B²/μ₀
Poynting S = E×B/μ₀
Intensity I = E·B/μ₀ = c·u
$$u_E = \frac{1}{2}\varepsilon_0 E^2, \quad u = \varepsilon_0 E^2$$$$S = c\varepsilon_0 E^2, \quad I = \frac{1}{2}c\varepsilon_0 E_0^2$$How to Use
- Enter the electric field E (V/m) and/or magnetic field B (T).
- The calculator returns energy densities and the Poynting/intensity.
Case Studies
Sunlight intensity
Solar constant ≈ 1361 W/m².
u = I/c ≈ 1361/3e8 ≈ 4.5×10⁻⁶ J/m³.
E_rms = √(u/ε₀) ≈ 720 V/m.
FAQ
Why are electric and magnetic energy densities equal?
In a plane EM wave E and B are linked by E = c·B, and with ε₀μ₀c² = 1 this makes ½ε₀E² = B²/(2μ₀).
What is the Poynting vector?
It points in the direction of propagation and its magnitude is the power per unit area (intensity) carried by the wave.
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References
Content review: Calculatorism Science Team. Results are for reference only; please refer to the relevant authorities for the official figures.