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# EM Waves in Dielectrics and Conductors - Electromagnetic Theory, CSIR-NET Physical Sciences Physics Notes | EduRev

## Physics for IIT JAM, UGC - NET, CSIR NET

Created by: Akhilesh Thakur

## Physics : EM Waves in Dielectrics and Conductors - Electromagnetic Theory, CSIR-NET Physical Sciences Physics Notes | EduRev

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 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? 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  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 I2R (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  159 docs

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