Electromagnetic waves in dielectrics – Compare velocity and wavelength with free space As compared to their values in free space, how do the phase velocity and wavelength of an electric wave change when it propagates in a lossless dielectric medium (relative permittivity ε_r > 1)?

Introduction:
Basic wave propagation in materials links phase velocity, frequency, and wavelength to material constants. Recognizing how dielectric loading changes velocity and wavelength is fundamental for transmission lines, antennas in substrates, and microwave component sizing.

Given Data / Assumptions:

• Lossless dielectric with relative permittivity ε_r > 1 and μ_r ≈ 1.
• Angular frequency ω the same in all media; frequency f is invariant across boundaries.
• Free-space values denoted with subscript 0.

Concept / Approach:

The phase velocity in a dielectric is v = c / √(ε_r μ_r) ≈ c / √ε_r. Since f is constant, the wavelength is λ = v / f = λ_0 / √ε_r. Therefore, both v and λ are reduced compared with free space when ε_r > 1. This is why microstrip/stripline physical lengths are shorter than their air-line counterparts for the same electrical length.

Step-by-Step Solution:

Verification / Alternative check:

Practical PCB calculations use effective ε_eff to shorten lines to a fraction of the free-space wavelength, confirming reduced v and λ.

Why Other Options Are Wrong:

Options A/D/E contradict v ∝ 1/√ε_r; option B reverses the trend. Option E keeps velocity unchanged which is untrue for ε_r > 1.

Common Pitfalls:

Confusing group and phase velocity; assuming frequency changes across media (it does not).

Final Answer:

both velocity and wavelength in dielectric are smaller.