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Basic Electromagnetism: Course Outline

Electromagnetism is a branch of physics which involves the study of the electromagnetic force, a type of physical interaction that occurs between electrically charged particles.

Course Outline

  • Vector algebra.
  • Vector operations.
  • Vector algebra.
  • Component form.
  • Triple products.
  • Position.
  • Displacement and separation vectors.
  • How vector transform.
  • Differential calculus. 
  • Ordinary derivatives.
  • Gradient. 
  • The operator.
  • The divergence.
  • Product rules.
  • Second derivatives.
  • Integral calculus.
  • Line, surface and volume integrals.
  • The fundamental theorem of calculus.
  • The fundamental theorem for divergences.
  • The fundamental theorem for curls.
  • Integration by parts.
  • Curvilinear coordinates.
  • Spherical polar coordinates.
  • Cylindrical coordinates.
  • The Dirac delta function.
  • The divergence of r/r2.
  • The one dimensional Dirac delta function.
  • The three dimensional delta function.
  • The Theory of vector fields:
  • The Helmholtz theorem.
  • Potentials.
  • Electrostatics.
  • The electric field.
  • Introduction, Coulomb’s law.
  • The electric field.
  • Continuous charged distributions.
  • Divergence and curl of electrostatic fields.
  • Field lines.
  • Flux and Gauss’s law.
  • The divergence of E.
  • Application of Gauss’s law.
  • The curl of E.
  • Electric potential.
  • Introduction to potential.
  • Comments on potential.
  • Poisson’s and Laplace’s equations.
  • The potential of a localized charged distribution.
  • Electrostatic boundary conditions.
  • Work and energy in electrostatics. 
  • The work done to move a charge.
  • The energy of a point charge distribution.
  • Comments on electrostatic energy.
  • Conductors: Basic properties.
  • induced charges.
  • Surface charge and force on a conductor.
  • Capacitors.


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Course Outline

  • Special techniques.
  • Laplace’s equation in one dimension.
  • in two dimensions.
  • and in three dimensions.
  • Boundary conditions and Uniqueness theorems.
  • Conductors and seconds uniqueness theorem.
  • The methods of image.
  • The classic Image problem.
  • Induced surface charge.
  • Force and energy.
  • Other image problems.
  • Separations of variables.
  • Cartesian coordinates.
  • Spherical coordinates.
  • Multipole expansion.
  • Approximate potential at large distance.
  • The monopole and dipole terms.
  • Origin of coordinates in multipole expansions.
  • The electric field of a dipole.
  • Electric Fields in Matter.
  • Polarization.
  • Dielectric.
  • Induced dipoles.
  • Alignment of polar molecules.
  • Polarization.
  • The field of a polarized object.
  • Bound charges.
  • Physical interpretation of bound charges.
  • The field inside a dielectric.
  • The electric displacement.
  • Gauss’s law in the presence of dielectrics.
  • A deceptive parallel.
  • Boundary conditions.
  • Linear dielectrics.
  • Susceptibility.
  • Permittivity.
  • Dielectric constant.
  • Boundary value problems with linear dielectrics.
  • Energy in dielectric systems.
  • Forces on dielectrics.
  • Magnetostatics.
  • Lorentz force law.
  • Magnetic fields.
  • Magnetic forces.
  • Currents.
  • Biot-Savart law.
  • Steady current.
  • The magnetic field of a steady current.
  • The divergence and curl of B.
  • Straight-line currents.
  • Applications of Amplere’s law.
  • Comparison of magnetostatics and electrostatics.
  • Magnetic vector potential.
  • The vector potential.
  • Magnetostatic boundary conditions.
  • Multipole expansion of the vector potential.