Mathematics

ETTORE MAJORANA
ETTORE MAJORANA

The aim of the course is to provide the basic theoretical understanding of classical electromagnetism.

Expected results: the ability to lay out and solve standard exercises on electrostatic, magnetostatic, slowly varying electric and magnetic fields.

Acquired knowledge: after passing the exam, the students will be able to profitably follow advanced courses in theoretical physics.

Acquired competences: besides learning the fundamental physics laws of electromagnetism, the students will develop the specific skills needed to address and solve scientific problems via analytical methods, in order to study, model and understand classical electromagnetic phenomena.

https://corsidilaurea.uniroma1.it/it/users/ettoremajoranauniroma1.it

General objectives: the aim of the course is to introduce the fundamental theoretical notions for the study and understanding of classical electromagnetism.

Specific objectives
1. Knowledge and understanding: at the end of the course the student will know the fundamental equations of electromagnetism (Maxwell's equations) and will be able to follow advanced courses in theoretical physics.
2. Applying knowledge and understanding: students who have passed the exam will be able to set up and solve standard exercises based on electrostatics, magnetostatics, slowly varying electric and magnetic fields.
3. Making judgements: in addition to learning the fundamental physical laws that govern electromagnetic phenomena, students will develop technical-scientific reasoning skills and analytical problem-solving skills, useful for studying, modeling and understanding the fundamental principles of classical electromagnetism .
These qualities and abilities will be verified periodically during the course with classroom discussions of a wide range of application examples and the resolution of typical problems.
4. Communication: students who have passed the exam will have developed the ability to communicate concepts, ideas and methodologies of classical electromagnetism.
5. Learning skills: the knowledge acquired will allow students to approach, individually or via other courses, more specialized and advanced aspects of classical electromagnetism.

a) Calculus: the content of the courses Analisi Matematica 1 and 2 is essential,
namely differential equations with more variables, line integrals differential forms, scalar and vector fields.
b) The knowledge foreseen by the course Fisica 1 is essential. The fundamental laws of dynamics, work, potential energy and Galilaean transformations.

Part I Electrostatics (50 hs)

1- Calculus basics
2- Electrostatics in vacuum
3 - Conductors
4 - Dielectrics

Part II Electromagnetism
5 - Stationary electric currents
6 - Magneto-statics in vacuum
7 - Variable Electric and magnetic fields
8 - Electromagnetic radiation and special relativity (brief notes)

Basic texts:
- Fisica II. Elettromagnetismo. Ottica, C. Mencuccini e V. Silvestrni, Ed. CEA
- Fisica generale Elettromagnetismo, S. Focardi, I.G. Massa, A. Uguzzoni e M. Villa, Ed. CEA
- Fisica II, di P. Mazzoldi, M. Nigro, C. Voci, Ed. EdiSES
- Notes in pdf format

For specific topics or deepening:
La Fisica di Berkeley. Vol. 2.
Classical Electrodynamics, John David Jackson, Wiley
Introduction to Electrodynamics, David J. Griffiths, Prentice Hall

Frontal classes using the blackboard at the end of each week exercises will be provided to the students.
The discussion of the exercises will be done in the class involving the students upon voluntary base.

Optional but recommended

The exam is divided in two sections. The first part is written and consists of solving exercises and the second is oral. On the e-learning the infos on the topics dealt in the classes are detailed, that is a guide to the skills needed for the written section.

The first section (written) consists of two exercises, one on electrostatics and the other on electromagnetism.
Each exercise can be scored up to 15/16, assigned upon one or more questions.
The written section lasts 3hs and is intended passed with a score that is at least 16/30.
The written section of the exam can be substituted by two short written tests, each one lasts 2hs, during the period of the course.
The first of these ongoing tests is in the middle of the course and the second close to the end. If the average score is > 18/30, this value is assumed as a written exam score.

The oral section of the exm consists of two questions on the two parts of the course.
The student must be able to repeat a mathematical demonstration treated during the course or use the strategies outlined during the course to explain the result on a given topic.

The evaluation of the oral part will consider the clearness and the appropriateness of the exposition.
After the average of written and oral scores, the exam is passed if this number is ≥ 18/30 and laude is assigned if this number is ≥ 31/30

The nature of displacement current

The Coulomb gauge

The Maxwell equations

Vector potential

The Ohm Law

Electromagnetic waves