## Paper Description

This course completes the standard framework of classical electromagnetism.

Electrodynamics formulated in terms of scalar and vector potentials, mechanical conservation laws for electromagnetism and an introduction to the theory of electromagnetic radiation.

Prerequisites:
PHSI 332

This paper consists of 15 lectures and 6 tutorials. There are 3 assignments.

Assesment:
Final Exam 70%, Assignments 30%

Important information about assessment for PHSI425

Course Coordinator:
Dr Terry Scott

After completing this paper students are expected to have achieved the following major learning objectives:

• Be able to recast the electric and magnetic fields in terms of scalar and vector potentials and to recast Maxwell’s equations in terms of these potentials.
• Understand the concept of an electromagnetic gauge, in particular to understand the use and importance of the Coulomb and Lorentz gauges. To be able to perform simple gauge transformations.
• Understand the conservation of energy and linear momentum in the interaction between electromagnetic fields and matter. To be able to use the Poynting vector to find the energy density, linear momentum density, and angular momentum density of a system of electromagnetic fields, charges, and currents.
• Understand the concept of retarded time and retarded scalar and vector potentials. To be able to show that these potentials satisfy the appropriate Laplace equations.
• Understand the Lienard-Wiechert potentials as special cases of retarded potentials. To understand the physical significance of these potentials and be able to use them to analyse simple configurations of charges and currents.
• Understand the production of electromagnetic radiation by accelerating charges.
• To be able to derive and analyse the fields radiated by oscillating electric and magnetic dipoles.

Topics:

• Review: Theory of vector fields and the Helmholtz theorem.
• Electrostatic multipole expansion.
• Magnetic vector potential.
• Magnetostatic multipole expansion
• Energy conservation in electromagnetic interactions, Poynting’s theorem, the Poyting vector.
• Conservation of linear momentum, the Maxwell stress tensor. Conservation of angular momentum.
• Maxwell’s equations in terms of the scalar and vector potentials. Gauge transformations. The Coulomb and Lorentz gauges.
• Retarded potentials.
• The Lienard-Wiechert potentials.
• Electric and magnetic fields from Lienard-Wechert potentials.
• Radiation from an arbitrary source.
• Power radiated by a point charge.

Resources:
Textbook: Griffiths, D.J. Introduction to Electrodynamics, Fourth edition

## Details

Electromagnetic potentials, mechanical properties of the electromagnetic field and their conservation laws, the Maxwell stress tensor, electromagnetic gauges, retarded potentials, Lienard-Wiechert potentials, fields of accelerating charges, and radiation.

Paper title Advanced Electromagnetism PHSI425 Physics 0.0833 10 points First Semester \$653.49 \$2,757.23
Limited to
BSc(Hons), PGDipSci, MSc
Contact
terry.scott@otago.ac.nz
Teaching staff
Dr Terry Scott
Textbooks
Griffiths, D.J. Introduction to Electrodynamics, Fourth edition.
Global perspective, Interdisciplinary perspective, Lifelong learning, Scholarship, Critical thinking, Information literacy, Self-motivation, Teamwork.
Learning Outcomes
After completing this paper students are expected to:
1. Be able to recast the electric and magnetic fields in terms of scalar and vector potentials and to recast Maxwell's equations in terms of these potentials
2. Understand the concept of an electromagnetic gauge, in particular to understand the use and importance of the Coulomb and Lorentz gauges and be able to perform simple gauge transformations
3. Understand the conservation of energy and linear momentum in the interaction between electromagnetic fields and matter and be able to use the Poynting vector to find the energy density, linear momentum density and angular momentum density of a system of electromagnetic fields, charges and currents
4. Understand the concept of retarded time and retarded scalar and vector potentials be able to show that these potentials satisfy the appropriate Laplace equations
5. Understand the Lienard-Wiechert potentials as special cases of retarded potentials, understand the physical significance of these potentials and be able to use them to analyse simple configurations of charges and currents
6. Understand the production of electromagnetic radiation by accelerating charges
7. Be able to derive and analyse the fields radiated by oscillating electric and magnetic dipoles

## Timetable

### First Semester

Location
Dunedin
Teaching method
This paper is taught On Campus
Learning management system
None

Electromagnetic potentials, mechanical properties of the electromagnetic field and their conservation laws, the Maxwell stress tensor, electromagnetic gauges, retarded potentials, Lienard-Wiechert potentials, fields of accelerating charges, and radiation.

Paper title Advanced Electromagnetism PHSI425 Physics 0.0833 10 points First Semester Tuition Fees for 2020 have not yet been set Tuition Fees for international students are elsewhere on this website.
Limited to
BSc(Hons), PGDipSci, MSc
Contact
terry.scott@otago.ac.nz
Teaching staff
Dr Terry Scott
Textbooks
Griffiths, D.J. Introduction to Electrodynamics, Fourth edition.
Global perspective, Interdisciplinary perspective, Lifelong learning, Scholarship, Critical thinking, Information literacy, Self-motivation, Teamwork.
Learning Outcomes
After completing this paper students are expected to:
1. Be able to recast the electric and magnetic fields in terms of scalar and vector potentials and to recast Maxwell's equations in terms of these potentials
2. Understand the concept of an electromagnetic gauge, in particular to understand the use and importance of the Coulomb and Lorentz gauges and be able to perform simple gauge transformations
3. Understand the conservation of energy and linear momentum in the interaction between electromagnetic fields and matter and be able to use the Poynting vector to find the energy density, linear momentum density and angular momentum density of a system of electromagnetic fields, charges and currents
4. Understand the concept of retarded time and retarded scalar and vector potentials be able to show that these potentials satisfy the appropriate Laplace equations
5. Understand the Lienard-Wiechert potentials as special cases of retarded potentials, understand the physical significance of these potentials and be able to use them to analyse simple configurations of charges and currents
6. Understand the production of electromagnetic radiation by accelerating charges
7. Be able to derive and analyse the fields radiated by oscillating electric and magnetic dipoles

## Timetable

### First Semester

Location
Dunedin
Teaching method
This paper is taught On Campus
Learning management system
None