# 28000 - General Physics T-2 (L-Z)

## Learning outcomes

At the end of the course, students have basic knowledge of electromagnetism both in vacuum and in matter, useful for applications to be studied in forthcoming teaching programs. Furthermore, students possess main concepts of vector field analysis. In particular, students are able to -Understand the physical meaning of fundamental law of electromagnetism. -Apply general concepts to particular cases in order to solve simple problems.

## Course contents

Introduction

Interactions and forces. The electric field. Brief overview of vector analysis: gradient, line, surface and volume integrals, curl and Stokes theorem, divergence and Gauss theoreme, Helmoltz theorem.

Electric field in vacuum

The electric charge, Coulomb's law and principle of superposition. Divergence and curl of the electrostatic field E. Gauss and Stokes theorem. Potentials, Poisson's and Laplace's equation. Multipole expansion (optional subject). Work and energy in electrostatics.

Electric field in matter

Conductors and dielectrics, basic properties. Conductors in the electric field: induced charge, surface charge and force on a conductor. Capacitors. Laplace's equations: boundary conditions and uniquesness theorem. The method of images (optional subject). Dielectrics. Induced dipoles. Polarization. The field of a polarized insulator. Bound charges and their interpretation. The electric displacement D, linear dielectrics, susceptibility, Permittivity and dielectric constant. Boundary conditions. Energy in dielectrics systems.

Moving point charge and curren. Volume current density. Continuity equation. Ohm's law. Electromotive force. Joule heating law. Circuits.

Magnetostatics

The Biot-Savart Law. Magnetic field B in vacuum. Divergence and curls of B. Ampère's law. Magnetic vector potential A. Boundary conditions. Multipole expansion of the vector potential (optional subject). Magnetic field in matter. Magnetization. The auxiliary field H. Diamagnets, Paramagnets, ferromagnets. Linear and nonlinear media. Permeability and Susceptibility.

Electromotive force. Motional emf. Faraday's and Lentz's law. Inductance. Energy in magnetic fields.

Maxwell's Equations

Need for dispacement current and symmetries in Maxwell's equations. Magnetic charge. Maxwell's equations in matter. Boundary conditions for E,D,B,H. The potential formulation. Gauge transformations. Coulomb Gauge and Lorentz Gauge. Lorentz Force law in potential form. Energy conservation and Poynting's theorem. Electromagnetic waves in vacuum.

Any university book on Electromagnetism.

Examples of some italian books:

• P. Mazzoldi, M. Nigro, C. Voci: Elementi di Fisica - Elettromagnetismo e Onde - Casa editrice EdiSES;
• S. Focardi, I. Massa e A. Uguzzoni: Fisica Generale - Elettromagnetismo, Casa Editrice Ambrosiana;
• C. Mencuccini, A. Silvestrini: Fisica II - Liguori Editore;
• Giancoli: Fisica 2, Casa Editrice Ambrosiana.

Some italian books translated from english:

• Resnik, Holliday, Krane: Fisica 2 - Casa Editrice Ambrosiana;

A good English book: David J. Griffiths, Introduction to Electrodynamics, Cambridge University Press.

## Teaching methods

Lectures: theory and exercises. Classes are not mandatory, but strongly recommended.

## Assessment methods

Written and oral exam.

During the written test, the use of books, notes and pocket is not allowed. No electronic media can be used.

The written test is designed to verify the skills acquired in solving problems concerning the arguments addressed in the course. A positive judgment (> 18/30) allows the sutdent to access to the oral examination.

The validity of the written test is limited to the same examination session.

## Teaching tools

A tutor is available to help the students with exercises.

Latest News and FAQ sections can be found in the homepage of the lecturer.

## Office hours

See the website of Cristian Massimi