PHY350: Electromagnetic Theory

InstructorArun ParamekantiAssociate Professor, Physics

What is Electrodynamics?

1. How do moving or static charges interact with each other?

2. How do they interact with radiation?

3. How does a system of moving charges lead to radiation?

...

Maxwell’s Equations

ε0"∇ · "E("r, t) = ρ("r, t)

1µ0

"∇× "B("r, t)− ε0∂ "E("r, t)

∂t= "J("r, t)

!∇× !E(!r, t) +∂ !B(!r, t)

∂t= 0

!∇ · !B(!r, t) = 0

How sources produce E/B fields:

Constraints on E/B fields:

Particle Dynamics

Dynamics of charges not specified at this stage, we could supplement Maxwell’s

equations with Newton’s laws or the laws of quantum mechanics for particles

We will not pursue this aspect in this course

Why is it interesting?

1. Fundamental Viewpoint: First example of a relativistic theory First example of “unification” of forces First example of a gauge theory Leads to a unified description of electrostatics, magnetism, optics, radiation from moving charges

2. Applications: Antennas, Motors, Fibre Optics, Superconductors, Particle accelerators, Astrophysical plasmas, Photonic band gap materials, Lasers, Ultracold atomic systems

Begin with static case

Assuming sources and fields have no time dependence simplifies Maxwell’s equations

Electrostatics

Magnetostatics∇ · !B(!r) = 0

1µ0

!∇× !B(!r) = !J(!r)

∇× !E(!r) = 0

ε0!∇ · !E(!r) = !ρ(!r)

Outline

1. Electrostatics:

Review - notion of electric field and electrostatic potential, Gauss’s law, conductors/capacitors

Poisson and Laplace equations, boundary value problems, uniqueness

Solving Laplace equation via method of images, separation of variables

Multipole expansion for the electrostatic potential

Electric dipoles

Electric fields and induced dipoles in matter

Outline

2. Magnetostatics -

Review - notion of magnetic field and magnetic vector potential, current elements and loops, Biot-Savart and Ampere law

Multipole expansion for the vector potential

Magnetic dipoles

Magnetic fields and induced magnetic dipoles in matter

Outline

3. Dynamics -

Review - Maxwell’s equations

Electromagnetic waves in vacuum and in matter

Waves at a vacuum-matter interfaces - reflection, refraction

Energy-Momentum

Potentials and gauge transformations

Textbook: D. J. Griffiths, Introduction to Electromagnetism, 3rd Edition

Reference: Feynman Lectures, Vol.2

Roughly: Chapters 3-8 of Griffiths, Parts of Chp 9,10,11

Lectures: M10, W10 (MP137)Tutorials: R9, R1 (MP137)

What should you expect to take away from the course?

1. Understand implications of laws of electrodynamics

2. Learn mathematical aspects of solving Maxwell’s equations

3. Appreciation of classical theory of fields

What I will do1. Will use the blackboard2. Will derive results3. Will discuss some problems from the text4. Will assign problems from the text for homework

What you need to do1. Stop me in class if something is unclear or wrong2. Solve problems: Only way to learn3. Register on Blackboard4. Participate in lectures/tutorials

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Homework: Problem sets - 20%

Midterm Exam (2): 40% Oct 4, Nov 17

Final Exam: 40%

Exams: One page (both sides) formula sheet permitted

No late submission

H1N1 preparednesshttp://www.preparedness.utoronto.ca

Missed term workIf you miss homework submission, midterm:. Show me a note from the doctor. Weight will be moved to the final exam. If you are at home on account of illness but wish to send in completed term work, you can scan and email it to the TA

Arun Paramekanti (Instructor)Office: MP1006Email: arunp@physics.utoronto.caOffice Hours: By appointment (for now)

Ganesh Ramachandran (TA)Email: gramach@physics.utoronto.ca

Email: Please put “PHY350” in subject

Open Door (for now)