Wave Speed in a Material Medium
In a homogeneous linear medium with permittivity epsilon and permeability mu, the phase speed is 1/sqrt(mu epsilon). Relative material parameters compare this speed with c.
Why this shows up in the exam
Finding wave speed in dielectrics · Determining relative permittivity from measured speed · Comparing travel times through different materials
Learn the idea
Permittivity and permeability set the speed of an electromagnetic wave in a medium. A material's electric and magnetic responses delay the coupled field changes. Larger permittivity or permeability therefore lowers the wave speed compared with vacuum.
🧠 Memory hook: More electric or magnetic response means less speed.
Get this one clearly and it pays off every single time it shows up in the paper. 🎯
Formulas & facts to keep ready
- v = 1/sqrt(mu epsilon) — electromagnetic-wave speed in a linear medium
- v = c/sqrt(mu_r epsilon_r) — speed in terms of relative permeability and permittivity
- c/v = sqrt(mu_r epsilon_r) — speed ratio between vacuum and the medium
How to approach it
- 1Write mu = mu_r mu₀ and epsilon = epsilon_r epsilon₀
- 2Use v/c = 1/sqrt(mu_r epsilon_r)
- 3Check that a passive ordinary medium gives v no greater than c
Common slip-ups that cost marks
- •Using v = c/sqrt(epsilon_r) when mu_r is not one
- •Confusing absolute and relative material constants
- •Taking the square root twice when using a speed ratio
🌟 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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