# NASSP Self-study Review 0f Electrodynamics - PowerPoint PPT Presentation

1 / 53

NASSP Self-study Review 0f Electrodynamics. Created by Dr G B Tupper gary.tupper@uct.ac.za. The following is intended to provide a review of classical electrodynamics at the 2 nd and 3 rd year physics level, i.e. up to chapter 9 of Griffiths book, preparatory to Honours.

I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.

NASSP Self-study Review 0f Electrodynamics

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.

- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -

## NASSP Self-studyReview 0f Electrodynamics

Created by Dr G B Tupper

gary.tupper@uct.ac.za

The following is intended to provide a review of classical electrodynamics at the 2nd and 3rd year physics level, i.e. up to chapter 9 of Griffiths book, preparatory to Honours.

You will notice break points with questions. Try your best to answer them before proceeding on – it is an important part of the process!

### Basics

• Maxwell’s equations:

• Lorentz force:

### Basics

• Mathematical tools:

• Gauss’ Theorem

• Stokes’ Theorem

• Green’s function

### Basics

• Mathematical tools:

• Second derivatives

• Product rules

• Potentials

### Questions

• Where is “charge conservation”?

• Where is Coulomb’s “law”?

• Where is Biot-Savart “law”?

### Work done on charge

• Power (Lorentz)

• Now

• So

• Use Ampere-Maxwell

• Identity

• So

### Poynting’s Theorem

• Define

• Mechanical energy density

• Electromagnetic energy density

• Poynting vector

• EM fields carry energy

### Questions

• Problem: an infinite line charge along z-axis moves with velocity :

Determine

### Waves in vacuum

• Maxwell’s equations:

### Waves in vacuum

• Use Gauss & Ampere-Maxwell; wave equation

• Speed of light

• Monochromatic plane-wave solutions

constant

Transverse

### Questions

• What is the meaning of the wave-number ?

• What is the meaning of angular frequency ?

• What is the associated magnetic field?

Wavelength

Period

### Monochromatic plane-wave

• Energy density

• Poynting vector

• Momentum density

• Time average

• Intensity

### Questions

A monochromatic plane-polarized wave propagating in the z-direction has Cartesian components in phase:

.

In contrast, a circularly-polarized wave propagating in the z-direction has Cartesian components

• out of phase:

• Describe in words what such a circularly-polarized wave looks like. One of the two casess “left-handed”, and the other is “right handed” – which is which?

i

Determine the corresponding magnetic field.

Determine the instantaneous energy-density and Poynting vector.

### Electrostatics in matter

• Electric field polarizes matter

• Potential in dipole approximation

• Bound charge density

Polarization: dipole moment

per unit volume

### Electrostatics in matter

• Rewrite Gauss’ law

• Displacement field

• For linear isotropic media

Free charge density

Dielectric constant

### Magnetostaticsin matter

• Magnetic field magnetizes matter

• Vector potential

Magnetization: magnetic moment per

unit volume

### Magnetostaticsin matter;Dipole moment proof

• Picture

• Dipole approximation

• For arbitrary constant vector

• Therefore

=0

Q.E.D.

### Magnetostaticsin matter

• Bound current density

• Rewrite Ampere’s law

• Induction

• For linear isotropic media

• Free current density

### Electrodynamics in matter

• New feature

• Rewrite Ampere-Maxwell

### Electrodynamics in matter

• Maxwell’s equations

• Constitutive relations

• Linear isotropic media

### Electrodynamics in matter

• Boundary conditions

### Electrodynamics in matter

• Energy density

• Poynting vector

### Electromagnetic waves in matter

• Assume electrical neutrality

• In general there may be mobile charges; use

• Resistivity

Conductivity

### Electromagnetic waves in matter

• Maxwell’s equations

• For constant use Ampere-Maxwell

### Electromagnetic waves in matter

• Wave equation

• In an ideal insulator

• Phase velocity

• Plane wave solution

New

Index of refraction

### Questions

• What do you expect happens in real matter where the conductivity doesn’t vanish?

• Which is more basic: wavelength or frequency?

### Electromagnetic waves in matter

• Take propagation along z-axis

• Complex ‘ansatz’

• Substitution gives

• Solution

### Electromagnetic waves in matter

• Thus general solution is

Transverse

Phase

Attenuation!

Frequency dependant: dispersion

### Electromagnetic waves in matter

• Limiting cases

• High frequency

• Low frequency

Good insulator

Good conductor

Note: at very high frequencies conductivity is frequency dependant

### Electromagnetic waves in matter

• Magnetic field – take for simplicity

### Electromagnetic waves in matter

Good conductor

### Questions

What one calls a “good conductor” or “good insulator” is actually frequency dependant; i.e. is

or ?

Find the value of for pure water and for copper metal. Where does it lie in the electromagnetic spectrum in each case?

For each determine the high-frequency skin depth.

For each determine the skin depth of infrared radiation ( ).

In the case of copper, what is the phase velocity of infrared radiation?

In the case of copper, what is the ratio for infrared radiation?

### Frequency dependence

• Electric field polarizes matter

• Model

…dynamically

“Restoring force”

Driving force

### Frequency dependence

• Electromagnetic wave

• Rewrite in complex form

Natural frequency

### Frequency dependence

• Substitution of steady state solution

• Dipole moment

### Frequency dependence

• Polarization

• Complex permittivity

Number of atoms/molecules per unit volume

### Frequency dependence

• Even for a “good insulator”

• Low density (gases)

Absorption coefficient

Ignore paramagnetism/diamagnetism

### Frequency dependence

• Low density

Frequency dependent: dispersion

### Frequency dependence

Anomalous dispersion

### Electromagnetic waves in Plasma

• Electrons free to move; inertia keeps positive ions almost stationary

• Model

• Solution

Electron mass

No restoring force!

### Electromagnetic waves in Plasma

• Current density

• Conductivity

Electron number density

Drude model

### Electromagnetic waves in Plasma

• Electron collisions rare, so dissipation small

• Recall for conductor

Purely imaginary!!

### Electromagnetic waves in Plasma

• As

• Above the plasma frequency: waves propagate with negligible loss

• Below the plasma frequency: no propagation, only exponential damping

Dispersion relation

Plasma frequency

F&F 2013 L46