古典電力學一
1. Electrostatics
Coulomb’s law, Gauss’s law
Scalar potential, Poisson and Laplace equations
Green’s theorem
Dirichlet and Neumann boundary conditions
Formal solution with Green’s function
Electrostatic potential energy and energy density, capacitance
2. Boundary-Value in Electrostatics
Method of image
Green function for a sphere
Orthogonal functions and expansions
Separation of variables, Laplace equations in rectangular coordinates
Laplace equations in spherical coordinates
Legendre equation and Legendre polynomials
Associated Legendre functions and spherical harmonics
Addition theorem for spherical harmonics
Laplace equations in cylindrical coordinates, Bessel functions
Expansion of Green function in spherical coordinates
Expansion of Green function in cylindrical coordinates
Eigenfunction expansions for Green functions
3. Multipoles, Electrostatics of Macroscopic Media, Dielectrics
multiple expansion
boundary-value problem with dielectrics
molecular polarizability and electric susceptibility
electrostatic energy in dielectric media
4. Magnetostatics
Biot and Savart law
Ampere’s law
vector potential
magnetic fields of a localized current, magnetic moment
macroscopic equations, boundary conditions for B and H
boundary-value problems in magnetostatics
5. Time-Varying Fields, Maxwell Equations, Conservation Laws
Faraday’s law of induction, displacement current, Maxwell equations
vector and scalar potential, gauge transformation
Green functions for the wave equation
derivation of the equations of the macroscopic electromagnetism
Poynting’s theorem and conservation of energy and momentum
conservation laws for macroscopic media
transformation properties of electromagnetic fields