Series
13 posts
An introduction to electrostatic equilibrium, Coulomb's law, vector superposition, and the electric field of fixed point charges in vacuum.
Study notes on signed electric flux, choosing Gaussian surfaces, and the connection between the integral and differential forms of Gauss's law.
Understand electric potential, voltage, and work, then connect the negative gradient to Poisson's equation and the potential of point charges.
Build a charge configuration one charge at a time to derive electrostatic interaction energy, the factor of one half, and energy stored in a vacuum electric field.
Learn why the field vanishes in a conductor at equilibrium, then derive the induced charges and potential of a sphere inside a neutral conducting shell.
Learn how Laplace's equation describes charge-free electrostatic potentials, from one-dimensional solutions to mean values, boundary conditions, and uniqueness.
Derive the potential, electric field, induced surface charge, force, and interaction energy for a point charge above an infinite grounded conducting plane.
Solve Laplace's equation in a grounded strip and rectangular pipe using separated modes, Fourier sine coefficients, and carefully stated boundary conditions.
An intuitive derivation of the far-field multipole expansion for a localized charge distribution, including monopole, dipole, quadrupole, origin dependence, and the ideal-dipole field.
An intuitive introduction to induced atomic dipoles, polarization density, and the bound surface and volume charges produced by a polarized dielectric.
An intuitive derivation of bound surface and volume charge densities in a polarized dielectric from its polarization field.
Deriving the electric displacement field D, its free-charge Gauss law, and its use in cylindrical and spherical dielectric examples.
Linear dielectrics, electric susceptibility and permittivity, followed by a complete solution for a charged conducting sphere surrounded by a dielectric shell.