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Playbook

Electromagnetic Waves

The wave equation, energy and intensity, and the order of the spectrum. Mostly recall and one-line calculations.

Questions in the bank
108
q/paper in 2025–26
0.85
Numeric answer
13%
Notes pages
4

Tier: Long tail

When you’ll see it

A wave's E or B field written out, an intensity or radiation pressure, displacement current, Maxwell's equations, or a band of the spectrum.

How this chapter is tested

A short chapter. Most questions need a single relation, such as E₀ = cB₀, I = ½cε₀E₀² or v = c/√(μᵣεᵣ), and then a careful cross product for a direction. The largest group is about the two fields of the wave themselves.

The pages start from displacement current and Maxwell's equations, which give the wave and its speed, then the fields, then the energy, intensity and pressure the wave carries, and end with the spectrum. The spectrum questions are pure recall of order, sources and uses.

Marks are lost on factors and directions: B written as cE instead of E/c, the average energy split wrongly between the two fields, a mirror given I/c instead of 2I/c, or the cross product taken in the wrong order. The pressure of light is the photon momentum of Dual Nature seen in bulk.

The sub-skills

The distinct skills inside the chapter, in the order to learn them.

  • Displacement current and wave speed

    Between capacitor plates the displacement current equals the conduction current; v = 1/√(με), so n = √(μᵣεᵣ), and the frequency stays fixed in a medium.

  • E and B of a plane wave

    E and B are perpendicular to each other and to the direction of travel, in phase, with B₀ = E₀/c and B along k × E.

  • Energy, intensity and pressure

    Average energy density ½ε₀E₀², shared equally by the two fields; intensity ½cε₀E₀², or P/4πr² for a point source; pressure I/c on an absorber and 2I/c on a mirror.

  • The spectrum

    The order from γ-rays to radio waves by increasing wavelength, and how each band is produced and used.

Traps to expect

Distractor shapes this chapter reuses. The Traps page covers the ones that cut across chapters.

  • B is E/c, not cE

    In SI units B₀ is tiny. An option that gives B the same number as E, or c times E, has skipped or inverted the division.

  • The cross product order

    B points along k × E, not E × k, and a wave travelling along −x puts −î in the product. The options usually offer both signs.

  • Counting the energy twice

    ½ε₀E₀² already holds both fields; the electric share alone is ¼ε₀E₀². Adding B₀²/2μ₀ on top doubles the answer.

  • Absorber or mirror

    Reflected light reverses its momentum, so a mirror feels 2I/c. Using I/c halves the answer.

Learn it before you drill it

This chapter has full teaching notes — foundations, worked examples, self-checks and a mastery check for each page. Read the notes once, then drill page by page below.

Electromagnetic Waves notes

Drill every Electromagnetic Waves question

108 questions from the bank, across 4 subtopics.

Drill the 108 questions

Drill one subtopic at a time

The 4 subtopics, in teaching order.

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