Electric and Magnetic Field Amplitudes
For a plane electromagnetic wave in a homogeneous isotropic medium, the instantaneous field magnitudes satisfy E/B = v when the fields are in phase. In vacuum the ratio is c. This relation also compares electric and magnetic forces on a moving charge.
Why this shows up in the exam
Finding magnetic amplitude from electric amplitude · Writing the companion field vector · Comparing electric and magnetic forces on a moving charge
Learn the idea
The electric and magnetic amplitudes of a plane wave are related by the wave speed. The two fields are not free to have unrelated strengths. Once the medium fixes the wave speed, specifying either electric or magnetic amplitude determines the other.
🧠 Memory hook: Field ratio equals wave speed.
Get this one clearly and it pays off every single time it shows up in the paper. 🎯
Formulas & facts to keep ready
- E₀/B₀ = v — amplitude relation in a medium
- E₀ = c B₀ — vacuum amplitude relation
- B = (1/omega)(k x E) — vector relation for a harmonic plane wave
- F_E/F_B = E/(u B) = v/u — force ratio for a charge moving perpendicular to B at particle speed u
How to approach it
- 1Determine whether the wave is in vacuum or a medium
- 2Use E₀ = v B₀ for the magnitude
- 3Use E cross B for field direction, then apply qE and quB if forces are asked
Common slip-ups that cost marks
- •Using c in a material medium without checking the speed
- •Using E₀ B₀ = c instead of E₀/B₀ = c
- •Using the particle speed in E/B instead of the wave speed
🌟 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.
More from Electromagnetic Waves
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Key mathematical relationships in electromagnetic waves include the connection between electric and magnetic field amplitudes, wave speed, wavelength, frequency, and the wave equation parameters.
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How Electromagnetic Waves Are Produced
Electromagnetic radiation is generated by accelerated charges or time-varying currents. In a source-free region, coupled time-varying electric and magnetic fields propagate without requiring a material medium.