Intensity and the Poynting Vector
The instantaneous Poynting vector is S = (1/mu)(E cross B). For a sinusoidal plane wave, intensity is the cycle average of its magnitude.
Why this shows up in the exam
Finding laser intensity from field amplitude · Calculating field amplitude from sunlight intensity · Determining energy-flow direction
Learn the idea
The Poynting vector gives electromagnetic energy flow per unit area per unit time. Imagine energy crossing a small window. The Poynting vector points through the window in the travel direction, while its magnitude tells how rapidly energy crosses each square metre.
🧠 Memory hook: Poynting points with E cross B.
Get this one clearly and it pays off every single time it shows up in the paper. 🎯
Formulas & facts to keep ready
- S = (1/mu)(E x B) — instantaneous energy-flux vector
- I = <|S|> — intensity as cycle-averaged energy flux
- I = (1/2) epsilon v E₀² — average intensity from peak electric field
- I = v B₀²/(2 mu) — average intensity from peak magnetic field
How to approach it
- 1Identify whether amplitudes are peak or rms
- 2Choose the electric-field or magnetic-field intensity form
- 3Check that the final unit is watt per square metre
Common slip-ups that cost marks
- •Omitting the one-half for peak sinusoidal amplitudes
- •Using rms values in a peak-value formula
- •Giving intensity a field direction rather than the E cross B direction
🌟 That's the whole idea — you've got this. Try the practice set below; every question you attempt makes it stick a little harder.
Original chapter practice
Original questions for this chapter, not past-paper questions or an exact mapping to this individual concept.
An electromagnetic wave in vacuum has wavelength 1 m. Take c = 3 x 10^8 m/s. Find its frequency in units of 10^8 Hz.
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