Intrinsic Impedance of a TM Wave

Introduction:
In electromagnetics, transverse magnetic (TM) waves are a type of electromagnetic wave that propagate in a direction perpendicular to the magnetic field. These waves have electric field components only in the direction of propagation. The intrinsic impedance is a fundamental property of electromagnetic waves that characterizes the relationship between the electric and magnetic fields.

Definition of Intrinsic Impedance:
The intrinsic impedance, often denoted by the symbol η (eta), is defined as the ratio of the magnitude of the electric field (E) to the magnitude of the magnetic field (H) in an electromagnetic wave. Mathematically, it can be expressed as:

η = E/H

Impedance of Free Space:
For free space, which is the absence of any medium, the intrinsic impedance is given by:

η0 = √(μ0/ε0)

where μ0 is the permeability of free space and ε0 is the permittivity of free space. The values of μ0 and ε0 are defined constants:

μ0 = 4π × 10^-7 H/m
ε0 = 8.854 × 10^-12 F/m

Substituting these values, we find:

η0 = √(4π × 10^-7/8.854 × 10^-12) ≈ 377 ohms

Comparison with Intrinsic Impedance of TM Waves:
The intrinsic impedance of TM waves depends on the properties of the medium through which they are propagating. TM waves can propagate in different media, such as dielectrics, conductors, or even vacuum. The intrinsic impedance of a TM wave is given by:

η = √(μ/ε)

where μ is the permeability of the medium and ε is the permittivity of the medium.

Since the permeability and permittivity of a medium are always positive, the intrinsic impedance of a TM wave will always be positive. However, it can have different values depending on the medium.

Conclusion:
The intrinsic impedance of a TM wave is not a constant value and can vary depending on the medium through which the wave is propagating. The correct answer to the given question is option C: Lesser than 377 ohms, as it is not always equal to the intrinsic impedance of free space (377 ohms).