58407 - Classical Electrodynamics

Learning outcomes

The course introduces the student to the aspects of electrodynamics not covered by the course of General Physics II, such as the foundations of electrodynamics, the multipole expansion of the electromagnetic field, the study of the energy balance and of the thermodynamics of polarized and magentized continua and the theory of constitutive relations.

Course contents

Introduction to the physics of continua.
Generalities on densities and current densities.
Generalities on balance laws and equations.
Discontinuity surfaces and junction conditions.

Mass, momentum, angular momentum and energy
balance laws and equations in physics of continua
and junction conditions thereof.

Irreversible thermodynamics of continua.
Principle of local equilibrium.
Balance law and equation for entropy and junction condition thereof.
Prigogine principle.
Clausius-Duhem inequality and junction condition thereof.
Method Colemann e Noll with applications.

Foundations of electrodynamics.
Electric charge, electric charge density and current density.
Lorentz force and Joule power laws.
Electric Gauss, Amp&egravere, magnetic Gauss and Faraday-Lenz laws.
Maxwell equations.
Charge conservation law and equation.
Electromagnetic momentum and energy density,
Maxwell stress tensor and Poynting vector.

Asymptotic radiation conditions.
Generalized Coulomb and Biot-Savart laws.
Quasistatic and radiation regimes.
Multipole moments of a charge distribution.
Multipole expansion of the electric and magnetic fields.

Electromagnetic field in the continuous matter.
Microscopic and macroscopic charge distributions.
Microscopic and macroscopic electric and magnetic induction fields.
Macroscopic Maxwell equations.
Free and bound charges.
Electric and magnetic polarizability.
Polarization and magnetization fields and their interpretation,
General discussion of constitutive relations.

Comoving formulation of Maxwell equations.
Comoving electric, electric induction, magnetic and magnetic induction fields.
Conductive electric current density.
Junction conditions of the fields.

Force and torque acting on and power supplied to a polarized and
magnetized continuum by an external electromagnetic field.
Electromagnetic momentum and energy density,
Maxwell stress tensor and Poynting vector
for a polarized and magnetized continuum.

Mass, momentum, angular momentum and energy balance laws and equations
for a polarized and magnetized continuum
and junction conditions thereof.

Clausius-Duhem inequality for a polarized and magnetized continuum
and junction condition thereof.

Electrodynamics of non dispersive fluids. Application
of the method of Coleman Noll for the determination of the constitutive
relations.
Linear approximation.
Introduction to magnetic hydrodynamics.

Dispersive homogeneous isotropic continua.
Fourier analysis of Maxwell equations
and the constitutive relations
Study of the frequency dependency of the dielectric constant.
Dispersion relations. Absorption, reflection and refraction in linear
dispersive continua.
Calculation of the dielectric constant as a function of the
frequency using Thompson atomic model.

Readings/Bibliography

J. D. Jackson, Classical Electrodynamics, John Wiley & Sons

W. K. H. Panofsky & M. Phillips, Classical Electricity and Magnetism, Addison Wesley Publishing Co.

Teaching methods

lectures and tutorials

Assessment methods

oral exam

Office hours

See the website of Roberto Zucchini