Energy, Intensity & Radiation Pressure
Light carries energy and pushes.
Lesson at a glanceShow the key points
- u_av = ½ε₀E₀² = B₀²/2μ₀ (40.7–40.8); equal electric and magnetic shares.
- I = u_av c = ½ε₀E₀²c (40.9).
- p = U/c (40.10): pressure I/c absorbed, 2I/c reflected.
Sunlight warms your face and pushes on solar sails. An electromagnetic wave carries both energy and momentum, shared equally between its electric and magnetic fields.
Energy density
In a small volume of the wave the energy is ½ε₀E² dV (electric) plus B²dV/2μ₀ (magnetic). With E = E₀ sin ω(t − x/c) and B = B₀ sin ω(t − x/c), and sin² averaging to ½:
Using E₀ = cB₀ and μ₀ε₀ = 1/c², the two terms are equal: on average the electric and magnetic fields carry the same energy.
A wave has E = (80 N/C) sin ω(t − x/c). How much energy is in a cylinder of cross-section 20 cm² and length 1.0 m along x?
Intensity
Intensity is the energy crossing unit area per unit time, perpendicular to the direction of travel. The energy in a cylinder of area A and length cΔt (uavcΔtA) crosses A in time Δt, so
Find the intensity of the wave above.
Momentum and radiation pressure
A portion of the wave carrying energy U also carries momentum
- Fully absorbed: the surface receives momentum U/c; the pressure is I/c.
- Fully reflected: the momentum reverses (p → −p), the surface receives 2U/c; the pressure is 2I/c.
Sunlight of intensity 1.36 kW/m² falls on a perfectly reflecting sail 100 m × 100 m, square-on. Find the force. Also find the peak electric field of sunlight.
- 1u_av = ½ε₀E₀² = B₀²/2μ₀ (40.7–40.8); electric and magnetic shares are equal.
- 2Intensity I = u_av c = ½ε₀E₀²c (40.9).
- 3Momentum p = U/c (40.10); pressure I/c absorbed, 2I/c reflected.
Check yourself
Keep exploring
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