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Energy and momentum of EM waves

EM wave fundamentals · Physics

Transverse wave

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A travelling wave ribbon. Raise the amplitude to make it taller, the frequency to make it faster.

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Study notes

A 100 W light bulb radiates uniformly in all directions. (a) Find the intensity at 2.0 m distance. (b) Find the radiation pressure on a small black (absorbing) surface there, and the force on 1 cm². (c) How many photons per second is that if the light averages 550 nm wavelength? Step 1: Intensity I = P/(4πr²) = 100/(4π × 4.0) = 100/50.27 ≈ 1.99 W/m². Step 2: Absorbing surface: pressure P_rad = I/c = 1.99/3.00×10⁸ ≈ 6.63×10⁻⁹ Pa. Force on 1 cm² = 10⁻⁴ m²: F = 6.63×10⁻⁹ × 10⁻⁴ ≈ 6.6×10⁻¹³ N — utterly negligible, which is why we never feel light pushing us. Step 3: Photon energy E = hc/λ = (6.63×10⁻³⁴ × 3.00×10⁸)/550×10⁻⁹ ≈ 3.62×10⁻¹⁹ J. Photons per second through 1 m² = I/E = 1.99/3.62×10⁻¹⁹ ≈ 5.5×10¹⁸ — an enormous number of tiny packets, which is why the wave picture works so well for everyday intensities.

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