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
� � � � � � � � �
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: [email protected] Hours: By appointment (for now)
Ganesh Ramachandran (TA)Email: [email protected]
Email: Please put “PHY350” in subject
Open Door (for now)
Top Related