The Poynting Vector and Radiation Pressure
The cross product of the electric and magnetic fields gives the energy flowing through unit area per second, and the same wave carries momentum. Light therefore pushes on what absorbs it, twice as hard if the surface is a mirror.
What a learner can do afterwards
- Computes the intensity of a wave from its field amplitudes
- Relates the momentum carried by a wave to its energy and finds the pressure on a surface
- Explains why a reflecting surface feels twice the pressure of an absorbing one
1 · Read
Waves carry energy, and the Poynting vector S equals E cross B over mu0 says where it flows. For a plane wave S points along the travel direction and pulses at twice the field frequency. Averaging over a cycle gives the intensity I equals E0 B0 over 2 mu0. Double the field amplitude and the power per square metre quadruples.
Sunlight at Earth carries about 1360 watts per square metre, which implies an electric amplitude near 1000 volts per metre. That bridge turns abstract amplitudes into the warmth on your skin. Whenever a problem hands you amplitudes, reach for S first and average second.
Energy in motion means momentum: a pulse of energy U carries momentum U over c. An absorbing surface stops the pulse and takes U over c, while a mirror reverses it and collects twice that. Spread over time and area, that momentum rate is radiation pressure: I over c absorbed, twice that reflected.
Reflection doubles the push because the light reverses its momentum instead of merely stopping. The effect is tiny on human scales but sculpts comet tails and can drive reflective solar sails. Maxwell predicted it from theory alone before torsion balances measured it.
Energy flow points the way, and momentum delivers the push.
2 · Watch
Take it off screen
Where it sits
This opens up
8 questions wait behind this lesson, each with its answer explained. Every answer feeds the sky: stars light as they are learned, and dim when it is time to come back.