Electric and Magnetic Energy Density
The instantaneous electromagnetic energy density is the sum of electric and magnetic terms. For a plane wave, the field-amplitude relation makes these terms equal, and sinusoidal time averaging contributes the usual factor of one-half.
Why this shows up in the exam
Finding energy stored in an illuminated volume · Comparing electric and magnetic energy shares · Converting field amplitude to average energy density
Learn the idea
A plane wave stores equal average energy in its electric and magnetic fields. Energy moves back and forth through two field forms. In a plane wave, the electric and magnetic contributions are equal at each point in a simple linear medium, so either contribution is half the total.
🧠 Memory hook: Plane waves split field energy equally.
Get this one clearly and it pays off every single time it shows up in the paper. 🎯
Formulas & facts to keep ready
- u_E = (1/2) epsilon E² — instantaneous electric energy density
- u_B = B²/(2 mu) — instantaneous magnetic energy density
- u_E = u_B, u_total = epsilon E² = B²/mu — plane-wave equality and instantaneous total
- <u_total> = (1/2) epsilon E₀² — cycle-averaged total energy density for a sinusoid
How to approach it
- 1Decide whether the question asks instantaneous or average energy
- 2Calculate one field contribution with the matching field value
- 3Double one contribution for the plane-wave total
Common slip-ups that cost marks
- •Calling either field contribution the total energy
- •Mixing peak and instantaneous field values
- •Forgetting the time-average factor for a sinusoidal squared field
🌟 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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