電磁學上

This course deals with the fundamentals of classical electricity and magnetism.

Topics to be covered: (basically following the textbook)

1. Some preliminary math
How to generalize the fundamental theorem of calculus in higher dimension?
Gradient, divergence, curl, and the -operator
In curvilinear coordinates
Some vector identities and integrability criteria
Dirac’s delta function
Inner product of functions and Fourier transform
Helmholtz theorem

2. Electrostatics
Coulomb’s law
Gauss’s law
Poisson’s equation and Laplace’s equation
Boundary conditions
Work and energy in electrostatics
Conductors and capacitors

3. Solving Laplace’s equation
Uniqueness of solution
The method of images
Separation of variables
Using complex variables
Multipole expansion
Averaging property of the Laplacian, and numerical solution

4. Electric Fields in Matter
Polarization
The D-field and boundary conditions
Energy

5. Magnetostatics
The Lorentz force law
Biot-Savart law
Ampere’s law
The magnetic vector potential

6. Magnetic Fields in Matter
Torque and force on a magnetic dipole
Magnetization
The H-field and boundary conditions

7. Electrodynamics
Motional emf
Faraday’s law
Inductance
Energy in magnetic fields
Fixing Ampere’s law
Maxwell’s equations
Maxwell’s equations in matter
The boundary conditions

8. Conservation Law
The continuity equation for electric charges
Poynting’s theorem
Newton’s third law in electrodynamics
Momentum and Maxwell’s stress tensor
Conservation of momentum and angular momentum

9. Electromagnetic Waves
EM waves in vacuum- the wave equation
EM waves in matter
Reflection and transmission at an arbitrary angle of incidence
Absorption and dispersion
Physical origin of the index of refraction
Guided waves

10. Potentials and Fields
Working it out in terms of 4-potentials
Retarded potentials
Lienard-Wiechert potentials for a point charge
The fields for a moving point charge

11. Radiation
Dipole radiation
Rayleigh scattering, and earth’s blue sky
Point charge radiation
Radiation reaction

12. Electrodynamics and Relativity
Re-examining the concept of space and time
The Lorentz transformation
The concept of spacetime
Relativistic mechanics
How EM fields transform
Magnetism as a relativistic phenomenon