The document EM Waves in Dielectrics and Conductors - Electromagnetic Theory, CSIR-NET Physical Sciences Physics Notes | EduRev is a part of the Physics Course Physics for IIT JAM, UGC - NET, CSIR NET.

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In this lecture you will learn:

- Wave propagation in dielectric media
- Waves propagation in conductive media

**Review: Plane Waves in Free Space**

**Faraday’s Law:**

**Ampere’s Law:**

**Complex Wave Equation:** Assume:

For a plane wave in free space we know the E-field and H-field phasors to be:

**Waves in a Dielectric Medium – Wave Equation**

Suppose we have a plane wave of the form,

traveling in an infinite dielectric medium with permittivity ε

What is different from wave propagation in free space?

Faraday’s Law:

Ampere’s Law:

**Complex Wave Equation:** Assume:

**Waves in a Dielectric Medium – Dispersion Relation**

**Substitute the plane wave solution:**

in the complex wave equation:

To get:

**Refractive Index:**

**Define refractive index “n” of a dielectric medium as:**

**Waves in a Dielectric Medium – Velocity**

**Plane wave:**

**Dispersion relation:**

The velocity of waves in a dielectric medium is reduced from the velocity of waves in free space by the refractive index

- Velocity of waves in free space: c
- Velocity of waves in dielectric medium of refractive index n:

**Waves in a Dielectric Medium - Wavelength**

**Plane wave in a dielectric medium:**

Dispersion relation:

But the magnitude of the wavevector is related to the wavelength by the relation:

So for a dielectric medium we get:

The wavelength of plane waves in a dielectric medium is reduced from the wavelength of plane waves of the same frequency in free space by the refractive index

**Waves in a Dielectric Medium – Magnetic Field**

**Plane wave:**

Calculate the magnetic field:

**Waves in a Conductive Medium – Complex Permittivity**

**Suppose we have a plane wave of the form,**

traveling in an infinite medium with conductivity σ and permittivity ε

**Faraday’s Law:**

**Complex Wave Equation:**

**Waves in a Conductive Medium – Complex Refractive Index**

**Plane wave:**

**Dispersion relation:**

**Waves in a Conductive Medium – Complex Wavevector**

Plane wave:

**Complex wavevector: **

**What are the implications of a complex wavevector?**

**Wave decays exponentially with distance as it propagates**

**Waves in a Conductive Medium – Magnetic Field**

**Plane wave:**

**Calculate the magnetic field:**

Note: The E-field and the H-field are no longer in phase since ηeff(ω ) is complex

**Waves in a Conductive Medium – Power Flow**

**Plane wave:**

**Note that:**

**Poynting vector and time average power per unit area:**

**Time average power per unit area decays exponentially with distance because energy is dissipated in a conductive medium due to I ^{2}R (or J.E) type of losses and this energy dissipated is taken away from the plane wave**

**Loss Tangent and Dielectric Relaxation Time - I**

The complex wavevector is:

The complex refractive index is:

Loss tangent =

But the dielectric relaxation time was:

**⇒ Loss tangent **

**Loss Tangent and Dielectric Relaxation Time - II **

**There are two possible scenarios:**

High frequency and/or low conductivity case (e.g. lossy dielectrics)

The frequency is much greater than the inverse dielectric relaxation time

⇒The conductive medium does not have enough time to react to the electromagnetic wave

⇒No appreciable currents flow in the conductive medium

**Low frequency and/or high conductivity case (e.g. Imperfect metals)**

The frequency is much smaller than the inverse dielectric relaxation time

⇒The conductive medium has enough time to react to the electromagnetic wave

⇒Appreciable currents flow in the conductive medium

**Waves in a Conductive Medium – Lossy Dielectrics**

**Plane waves:**

**Lossy dielectric approximation:**

**Waves in a Conductive Medium – Imperfect Metals**

**Now consider the case when:**

The frequency is much smaller than the inverse dielectric relaxation time

⇒The conductive medium has enough time to react to the electromagnetic wave

⇒Appreciable currents flow in the conductive medium

These currents try to screen out the magnetic field and, therefore, prevent the electromagnetic wave from going into the conductor

**Waves in a Conductive Medium – Imperfect Metals**

**Imperfect metal approximation:**

**Waves in a Conductive Medium – Imperfect Metals**

**Due to current screening the wave decays within a few skin-depths:**

Since the wavelength λ inside the medium is , the wave hardly propagates one wavelength distance into the medium

The screening current density, given by is non-zero only in a layer of thickness equal to skin-depth δ near the surface

**Waves in a Conductive Medium**