GENERAL PHYSICS II

The teaching of General Physics II aims at studying the laws of electromagnetism and optics summarised in Maxwell's equations. Introduces the fundamentals of the theory of special relativity and emphasized the close connection with electromagnetism. The program also includes the handling of the covariant formulation of Maxwell's equations. Are finally treated the first elements of the classical theory (meaning not quantum mechanics) of the radiatio

Vector fields and differential operators (*)

Polar and axial vectors and their symmetries - gradient, divergence, curl and Laplace operator - Linear differential forms - Conservative fields, irrotational and solenoidal - Radial and central fields - Quadratic differential forms - Gauss' theorem - Theorem of Stokes - First and second identity of Green - the Helmholtz decomposition theorem - Laplace equation and properties of its solutions - vector identities for the operators gradient, divergence and curl.

Electrostatic interactions in vacuum and in matter

Conservation, quantization and relativistic invariance of electric charge - Coulomb's Law - Electrostatic field and its properties - Potential and electrostatic field produced by discrete and continuous charged distributions - Equations of Poisson and Laplace – Series expantion of multipole electrostatic potential - Motion of charges in electrostatic fields - The electric dipole - Interactions between a dipole and an electrostatic field - Energy and density of energy associated to the electric field - Electrostatic pressure - Conductors and insulators - Electrostatic equilibrium in homogeneous conductors - The Coulomb theorem- Power of the tips - Green's theorem of reciprocity - Conductors systems: capacitors - Forces acting between conductors - Boundary conditions and uniqueness theorems for electrostatics - the images method in the study of the interaction between a point charge with a conductor plain infinitely extended or with a conducting sphere - Potential and electrostatic field produced by polarization distributions assigned - Electrostatic field in the presence of homogeneous and isotropic linear dielectric - The electrical vectors D, E and P - Interaction between a point charge and a plan and infinitely extended dielectric - Potential and electrostatic field of a uniformly polarized sphere - Consequences arising from the assumption of deviation from strict dependence by the inverse square of the distance in the Coulomb law.

The electric current

Current density and equation of continuity - Laws of Ohm - Joule effect - Electromotive force - Resistors in series and parallel - Stress calculation of three-dimensional conductors - RC circuit.

Interactions magnetostatic in vacuum and in matter

The magnetostatic field - Lorentz force - Biot and Savart law - the magnetostatic field properties: the flow field and magnetostatic Ampere's theorem - Magnetic fields produced by simple current distributions - The laws of magnetostatic in local form - The vector potential and Laplace elementary law - Multipole expansion of the vector potential - The ideal magnetic dipole - Self and mutual inductance coefficients of circuits - Forces and moments acting on a current in a magnetic field - Magnetostatic Pressure - Motion of charges in magnetic fields - speed selector - Hall Effect - Cyclotron and mass spectrometer - Magnetization of homogeneous and isotropic bodies - Dia, para- and ferromagnetism from the microscopic point of view - The magnetic field produced by the magnetized material - Vector potential and magnetic field of a uniformly magnetized sphere - Extension of the laws of magnetostatic in matter - magnetic fields B, H and M.

Electric fields and magnetic variables

Electromagnetic induction - Lenz-Faraday-Neumann's law - Circuit RL - Energy and density of energy associated to a magnetic field - Resonant Circuit - Alternating current circuits - Displacement current - The laws of the electromagnetic field in the presence of matter - Propagation of signals in transmission lines - Examples of transmission lines: two-wire and coaxial cable - the laws of the electromagnetic field in the local form: Maxwell's equations - boundary conditions for the electric and magnetic vectors E and D B and H - potential of cem and gauge invariance - gauge Lorentz – Retarded potential- Poynting theorem - Plane and spherical waves in linear dielectrics - plane waves in conductors – Maxwell stress tensor.

Classical theory of radiation

Liénard and Wiechert potentials- the electromagnetic field produced by a charge in arbitrary motion - the electromagnetic field generated by a charge in uniform rectilinear motion - Radiation from accelerated charge at low speed - Larmor formula - Stability of the hydrogen atom - Radiation from charge having collinear velocity with the acceleration - bremsstrahlung - the law of force between two electric charges in motion - Synchrotron radiation - Liénard formula - Cherenkov radiation.

Special Relativity and elements of relativistic electrodynamics

Inertial reference frames and covariance of physical laws - Operational definition of measurements of space and time - Topological and metric simultaneity- Postulates of the special theory of relativity - Lorentz Transformations: dilation and length contraction durations – Space-time interval - Chronotope of Minkowski - Temporal order of events and spatial separation - Proper time - Twins paradox - Vectorial Lorentz Transformations - Transformations of speed and acceleration - Transformation of momentum, energy and forces - Aberration of velocity light and Doppler effect - Electromagnetism and special relativity: interaction between a moving charge and a current, interaction between current, potential and c.e.m. of a charge in uniform rectilinear motion - Lorentz transformations as rotations in space-time – Four-vectors space-time, velocity and acceleration - Four-vector current density - Transformations for the current intensity and the charge linear density - Four-vector potential - Tensor of the electromagnetic field – The Minkowski force - Transformations of c.e.m. - Covariant form of Maxwell equations - Four-vector density of force and tensor energy-momentum of c.e.m. - Relativistic motion of charges in uniform electric and magnetic fields - Photoelectric and Compton effects.

The physical and geometrical optics

Linear, circular and elliptical polarizations - Reflection and transmission of o.e.m .: normal and oblique incidence - Snell's law and Fresnel's equations - Polarization by reflection - Brewster's angle - Total reflection - Reflection of o.e.m. by a conductive surface - Law of reflection from a mirror in motion - Scattering of light - Interference between sources of correlated o.e.m. : Fresnel mirrors and interferometers - Thin Sheet - Diffraction of light - Fraunhofer phenomena - Cleft thin - Optical systems - Mirror plane, spherical and parabolic - the prism - The diopter spherical and flat - Thin and thick lenses- Fermat’s principle

Note: The performance of certain topics in lessons do not necessarily follow
the order given in this program.
(*) Some topics in this chapter, when it will be necessary, will be held during
the discussion of subsequent chapters

J.C. Maxwell : A Treatise on Electricity and Magnetism, Vol. 1 e 2

Dover Publications

S. Bobbio, E. Gatti : Elettromagnetismo, Ottica - Bollati Boringhieri

L. Lovitch, S. Rosati : Fisica Generale: Elettricità, Magnetismo, Elettromagnetismo,

Relatività ristretta, Ottica, Meccanica quantistica - C.E.A

P.Mazzoldi, M.Nigro, C. Voci : Elementi di Fisica, Vol. 2 – Edi SES

G. Piragino, G. Pisent : Fisica Generale e Sperimentale vol. II - Piccin

J.D. Jackson : Elettrodinamica classica - Zanichelli

E. M. Purcell : Elettricità e magnetismo – La fisica di Berkeley, vol. 2 - Zanichelli

R. Resnick : Introduzione alla relatività ristretta" - C.E.A., Milano

V. Barone : Relatività - Bollati Boringhieri

The student is free to choose any other text at the university level.