Guided Phase Constant in TEM Waveguide

The guided phase constant is an important parameter in the analysis of electromagnetic waves in a waveguide. It is defined as the ratio of the phase velocity of the wave in the waveguide to the speed of light in free space.

Formula

The formula for the guided phase constant is given as:

Beta = kc/ω

Where,
Beta is the guided phase constant
k is the wave number
c is the speed of light in free space
ω is the angular frequency

In a TEM (Transverse Electromagnetic) waveguide, the electric and magnetic fields are perpendicular to the direction of propagation of the wave. Hence, the wave does not have any longitudinal component.

Given, the phase constant of the waveguide as 2.8 units.

Solution

The wave number k is related to the phase constant by the formula:

k = β/√(εμ)

Where,
ε is the permittivity of the medium
μ is the permeability of the medium

For a TEM wave, the permittivity and permeability are constants and are the same as that of free space. Hence,

ε = ε0 = 8.85 x 10^-12 F/m
μ = μ0 = 4π x 10^-7 H/m

Substituting the given values in the formula for k, we get

k = β/√(εμ) = β/√(ε0μ0) = β/377

Substituting this value of k in the formula for the guided phase constant, we get

Beta = kc/ω = (β/377) c/ω = βc/(377ω)

Since the phase constant of the waveguide is given as 2.8 units, the guided phase constant is given by

Beta = 2.8c/(377ω)

Therefore, the correct answer is option A, i.e., 2.8.