28000 - General Physics T-2 (A-F)

Learning outcomes

The course deals with the fundamental concepts of the electromagnetism. The purpose is to give to the students the theoretical and experimental bases of the electromagnetic interaction.

Course contents

Introduction.

Brief overview of differential and integral calculus. The concept of field. Gradient of a scalar function, divergence and curl of a vectorial field. Gauss, Stokes and Helmotz theorems. Scalar and vector potentials. The Dirac delta function.

The electrostatic field in vacuum.

The electric charge. The Coulomb law and the electrostatic field.

Divergence and curl of electrostatic fields. The electric potential. The Poisson and Laplace equations. The multipole expansion of the potential. The monopole and dipole terms. The electrostatic energy.

The electrostatic field in matter.

The conductors. The induced charges. Basic properties of conductors. The electric capacity and the capacitors.

The dielectrics. Induced dipoles and alignment of polar molecules. The electric polarization. The bound charges and the charges of polarization. The D field. The divergence and the curl of D. The linear dielectrics. The electrostatic energy in dielectric systems.

The electric current.

The motion of electric charges and the electric current and the current density. The charge conservation and the continuity equation.

Magnetostatics.

The magnetic field, the magnetic forces and the Lorentz force law. Steady currents and the Biot-Savard law. Ohm's law. The electromotive force. The divergence and curl of the magnetic field B. The Ampère Law. The vector potential. Multipole expansion of the vector potential.

Magnetostatic fields in matter.

The magnetic dipole and the magnetization. Diamagnets, paramagnets and ferromagnets. Torques and forces on magnetic dipoles. The magnetization function. Effect of a magnetic field on the atomic orbits and the electronic spin. The bound currents.The field of a magnetized object. The auxiliary field H. Magnetic susceptibility and permeability. The linear media. The ferromagnetism.

Electrodynamics.

The electromotive forces and the Faraday's law. The mutual and the self inductance. The Joule effect. The energy in magnetic fields. Electrodynamics before Maxwell. The symmetry of the laws of nature and how Maxwell fixed up Ampère's law. The Maxwell's equations inside matter.

Scalar and vector potentials. Gauge transformations. The Coulomb gauge and the Lorentz gauge. The solutions of the Maxwell's equations in vacuum: the electromagnetic waves.

The Poynting's theorem and the continuity equation for energy. The Maxwell's stress tensor. Conservation of momentum.

Assessment methods

Written and oral exam.

Office hours

See the website of Gianni Vannini