GENERAL PHYSICS II

FIS/01 - 12 CFU - 1° Semester

Teaching Staff

GIUSEPPE RUSSO


Detailed Course Content

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



Textbook Information

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


Dover Publications

S. Bobbio, E. Cats: Electromagnetism, Optics - Basic Books Bollati

L. Lovitch, S. Rosati: General Physics: Electricity, Magnetism, Electromagnetism,

Special Relativity, Optics, Quantum Mechanics - C.E.A

P.Mazzoldi, M.Nigro, C. Items: Elements of Physics, Vol. 2 - Edi SES

G. Piragino, G. Pisent: General and Experimental Physics vol. II - Piccin

J.D. Jackson: Classical Electrodynamics - Zanichelli

E. M. Purcell: Electricity and magnetism - Berkeley Physics Course, Vol. 2 - Zanichelli

R. Resnick: Introduction to special relativity "- C.E.A., Milan

V. Barone: Relativity - Bollati Basic Books

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




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