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Physics · University

Electromagnetic waves and energy flow

In vacuum, plane electromagnetic waves have transverse electric and magnetic fields with E0=cB0. Both fields are perpendicular to propagation.

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Prerequisites

Vector calculus and sinusoidal waves.

Study notes

Vacuum waves

In vacuum, plane electromagnetic waves have transverse electric and magnetic fields with E0=cB0. Both fields are perpendicular to propagation.

Energy flux

The Poynting vector is S=(E×B)/μ0 in vacuum. Its direction gives electromagnetic energy flow in this model.

Intensity

For a sinusoidal vacuum plane wave, mean intensity is ε0cE0²/2. Peak and rms field conventions must not be interchanged unnoticed.

Dispersion

Phase speed ω/k and group speed dω/dk need not coincide in a dispersive medium. Vacuum propagation is a special nondispersive case.

Worked examples

In a vacuum plane wave, how are E and B oriented relative to propagation?

Maxwell plane-wave solutions have mutually perpendicular E, B and propagation directions.

Both are transverse

Use c=3×10^8 m/s. For B0=2×10^−6 T, find E0.

E0=cB0=600 V/m.

600 V/m

Check your understanding

  1. Which vector sets electromagnetic energy-flow direction in vacuum?

    1. Position alone
    2. E minus B
    3. E cross B
    4. E plus B without units

  2. If a sinusoidal electric-field amplitude doubles, by what factor does mean intensity change?

  3. For dispersion relation ω=ak², which is group speed?

    1. 2ak
    2. ak
    3. a/k
    4. Zero for all k

  4. For ω=2k² in consistent units at k=3, calculate group speed.

Answers and marking guidance

Answers and marking notes
  1. E cross B

    The Poynting vector is proportional to E×B.

  2. 4

    Mean intensity is proportional to E0².

  3. 2ak

    Differentiate ω with respect to k.

  4. 12 m/s

    dω/dk=4k=12 in the stated units.

Further reading and review references

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