The course provides methods for the study of elementary oscillatory phenomena, with particular reference to electromagnetic waves and optics; the student achieves a unitary vision of mechanical, electrical and electromagnetic phenomena.
Coulomb’s law. Electrostatic energy. The energy of a ionic crystal: NaCl. Hydrogen atom size estimate. Rutherford’s atomic model. The conservative nature of electric fields. Electrostatic potential. Gradient and curl. Electrostatic dipole. Sources of the electrostatic field: Gauss’ theorem. Divergence of vectorial fields. Conductors. Coulomb’s theorem. Faraday’s shield. Condensers. Energy density of the electrostatic field. Laplace’s and Poisson’s equations. Image method in electrostatics. Series and parallel connection. Electrostatics of dielectrics. Polarization charges. Electronic polarizability. Curie’s law. The Clausius-Mossotti equation. Lorentz’s force and magnetic field. Current density. Continuity equation. Stationary electric currents. Solenoidal fields. Drift speed and thermal speed. Electric resistance snd Ohm’s law. Motion of electric charges within electric and magnetic fields. Anderson’s experiment. Forces on conductors in magnetic fields. Magnetic dipole. Properties of stationary magnetic fields. Biot-Savart’s law. Ampère’s law. Maxwell’s equations for stationary fields. Vector potential. Gauge transformations. Coulomb’s gauge. Electrostatic analogies. Potential energy of magnetic dipoles. The Faraday experiments. The law od electromagnetic induction. Applications of Faraday’s law. Eddy currents. Alternating-current generator. Self and mutual inductance. Reciprocity. Magnetic energy. The Ampère-Maxwell equation. Maxwell’s equations. Solutions of Maxwell’s equation: electrodynamic potentials. Lorentz’s gauge. Wave equation. Maxwell’s equation in free space: propagation of electromagnetic fields. Plane waves. Spherical waves. Retarded potentials. Oscillating dipoles. The energy conservation law. Poynting’s vector. Momentum of electromagnetic fields. Radiation pressure. The origin of refractive index. The mathematics of interference and diffraction. Diffraction gratings. The law of geometrical optics. Rays. The law of reflection and refraction. Fermat’s principle. Image formation systems. Cartesio oval. Spherical lenses. This lens equation. Spherical and chromatic aberrations. Resolving power.