# 27215 - General Physics 2

## Learning outcomes

At the end of the course the student has the basis of classical elettromagnetism and of special relativity. She/he acquires the necessary abilities to solve simple physical problems.

## Course contents

Module 1

a) Elements of Differential and Integral Vector Calculus. Scalar and Vectoral Fields. The gradient operator. Flux and circulation of a vector field. Gauss' and Stokes' theorems.

b) Electrostatics. Coulomb's law. Electric field and electrostatic potential. Equipotential field lines and surfaces. Gauss law. Poisson equation. Dipole and multipole momenta. Electrostatic with conductrs. General problema of ectrostatic and Laplace's equation. Capacitors. Electrostatic energy. Electric field with Dielectrics.

c) Steady electric current. Intensity and density of electric current. Continuity equation. Ohm's and Joule's laws. Kirchhoff's laws.

d) Magnetostatics. The magnectic induction vector. Magnetic force on a current. Lorenz force. Biot-Savart law. Laplace formulae. Flux and circulation of magnetic field. Divergence and curl of the magnetic field. Vector Potential. Ampere equivalence theorem. Magnetic field and matter.

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

f) Maxwell equations. The Displacement current.

Module 2

Module1 and Module2 simple problem's solutions.

a) Solution of Maxwell equations with retarded potentials.

b) Waves. Wave equation. Plane and sperical waves. Electromagnetic waves. Velocity of propagation and Waves polarization. Field energy and field momentum: Poybting Vector. Radiation pressure. Dipole radiation and Larmor formula. Waves propagation in matter. Monocromaric and non monocromatic waves. Wave packets. Phase velocity and group velocity.

h) Limits of the classical electromagnetism. Photoelectric effect.

i) Radiation of a charged particle.

l) Special Relativity. Galileo Transformations and their incompatibility with Maxwell laws. Invariance of light speed. Lorentz Transformations. Velocity composition. Length contraction and time dilatation. Proper time. Relativistic dynamics. Mass-energy equivalence. Momentum and energy conservation. Scattering. Electromagnetism in relativity. 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) Mencuccini, Silvestrini, FISICA Elettromagnetismo e Ottica, Casa Editrice Ambrosiana

d) R. Resnick, Introduzione alla relativita' ristretta, Casa Editrice Ambrosiana

## Teaching methods

Lectures at the blackboard and solution of problems in the classroom.

## Assessment methods

Written test (lasting 3 hours) consisting in the solution of 3 simple problems with a minimum threshold (18/30), and then an oral examination of about 30 min. The results of the written test will hold for all the subsequent oral exams in the Session.

The final grade is the average of the written and oral tests.

During the course a couple of written tests (lasting 2 hours each) will be proposed (December and May) which, if positive (>=18/30), replace the written test for the summer exam session.

## Office hours

See the website of Paolo Capiluppi

See the website of Francesca Pozzi