27215 - General Physics 2

Learning outcomes

At the end of the course the student will know the basis of elettromagnetism and of special relativity and will obtain the necessary abilities for the solution of elementary problems.

Course contents

I module: ELECTROMAGNETISM

a) Differential and Integral Calculus of Vector Fields The gradient operator. Second order derivatives. Flux and circulation of a vector field. Gauss' and Stokes' theorems.

b) Electrostatics. Coulomb's law. Electric field and electric potential. Gauss theorem. Poisson equation. Dipole and multipoles. Conductors and capacitors. Electrostatic energy. Dielectrics.

c) Steady electric currents. Continuity equation. Ohm's and Joule's laws. Kirchhoff's laws.

d) Magnetostatics. Magnetic force on a current. Lorenz force. Biot-Savart law. Laplace equations. Flux and circulation of magnetic field. Potential vector. Ampere equivalence theorem. The magnetism of matter.

e) The laws of induction. The physics of induction and the Faraday law. Non conservative electric fields. Self-induction and mutual induction. The magnetic field energy.

f) Maxwell equations. The Displacement current. General solution with retarded potentials.

g) Wave. Wave equation. Plane and sperical waves. Electromagnetic waves. Waves polarization. Field energy and field momentum. Radiation pressure. Dipole radiation and Larmor formula. Waves propagation in matter. Monocromaric waves and real waves. Phase velocity and group velocity.

h) Limits of the classical electromagnetism. Photoelectric effect.

II module: SPECIAL RELATIVITY

1) Inertia and Relativity Principles. Galileo Transformations and their incompatibility with Maxwell laws and speed of light invariance. Lorentz
Transformations. Velocity composition. Length contraction and time dilation. Proper time. Minkowski diagrams, elements of space-time
geometry, light-cone and causality. Twins paradox. Introduction to flat 4-dimensional formalism: 4-vectors, Einstein sum convention and tensors.
Light Aberration. Doppler effect

2) Relativistic dynamics of the point particle. Mass-energy equivalence and mass-shell equation. Momentum and energy conservation. 4-mom4ntum,
4-force. Equations of motion. Scattering. Compton effect.

3) Electromagnetism in relativity. Electromagnetic tensor and Maxwell equations in 4D formalism. Lorentz 4-force. Transformations of E and B
fields.

Readings/Bibliography

a) Halliday, Resnick e Krane, FISICA 2, Casa Editrice Ambrosiana 

b) Amaldi et al., FISICA GENERALE, Zanichelli

c) Giacomelli e Gregorini, FISICA GENERALE - Elettromagnetismo e Ottica, La Nuova Italia Scientifica

d) Gettys et al., FISICA 2, Elettomagnetismo-Onde-Ottica, McGraw-Hill

e) Feynmann et al., "The Feynmann Lectures on Physics", Addison Wesley

f) Bruno, D'Agostino, Santoro, Esercizi di Fisica - Elettromagnetismo, Casa Editrice Ambrosiana

g) Special relativity course and exercises will be available, in PDF format, after the beginning of the lessons 

h) R. Resnick, Basic concepts in relativity and early quantum theory, Wiley, New York, 1992.

i) L. D. Landau and E. M. Lifshitz, Fisica Teorica, vol. 2: Teoria dei Campi, Editori Riuniti, Roma, 1976

Teaching methods

Lectures and exercises

Assessment methods

Written and Oral exam

Office hours

See the website of Loretta Gregorini

See the website of Francesco Ravanini