2^nd Year Electromagnetism Lecture Synopsis

Michaelmas Term

There are eight lectures in this term. Two per week beginning in 4^th week. The following summarizes the content of each lecture.

Lecture 1: Much is review of first year material. Forces on objects containing the property of electric charge. Vector Force field concepts. Electric Field of a charge distribution. Example of finite line of charge. Electric field of an elementary unit of charge. Divergence and curl of the electric field. The electric potential.

Lecture 2: Electric potential and Laplace’s equation. The meaning of Laplace’s equation in one, two, and three dimensions in Cartesian coordinates. Uniqueness theorems. Separation of variables and Boundary conditions and a two dimensional example of well-bounded solutions to Laplace’s equation.

Lectures 3 and 4: Electric field and electric potential boundary conditions at surfaces of highly conductive metals and at surfaces coated with fixed static charges. Laplace’s equation in cylindrical and spherical coordinates. Example in cylindrical coordinates. Solutions in spherical coordinates (Legendre polynomials). General solution of a charged sphere. Multiple expansion of the electric potential.

Lecture 5: Behaviour of a compass near a current carrying wire. Motion of point charges in electric and magnetic fields. Vector Magnetic fields due to arbitrary current density and a brief review of the uses of Ampere’s law. The curl and divergence of the magnetic field. Example of particle motion in a uniform static magnetic field. Revisit point charge motion near a current carrying wire. Use relativity to demonstrate that electric neutrality is frame dependent comparison of Lorentz transformations of charge density and current density to time and position from Special relativity.

Lecture 6: Magnetic field boundary conditions at surfaces with currents and for ideal metals (superconductors). The scalar magnetic potential. The magnetic Vector potential and why it is widely used and far more important to science than the magnetic scalar potential.

Lecture 7: Linear and Ferromagnetic materials. The H-field and magnetization M. Boundary conditions of B and H. Uses of magnetic scalar potential in boundary value problems. Problem solutions with Ferromagnetic materials. The energy density in magnetic and electric fields.

Lecture 8: Review of changing Electric and Magnetic fields. Maxwell’s equations. Wave solutions to Maxwell’s equations. The monochromatic electromagnetic wave in free space (plane waves). The energy in the Electric and Magnetic fields. The energy of the electromagnetic wave (Poynting Vector). Momentum carried by an EM wave.