28000 - General Physics T-2

Academic Year 2025/2026

  • Docente: Elena Cuoco
  • Credits: 6
  • SSD: FIS/01
  • Language: Italian
  • Teaching Mode: Traditional lectures
  • Campus: Bologna
  • Corso: First cycle degree programme (L) in Electrical Energy Engineering (cod. 6675)

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 (10 hours)

Interactions, forces, and the concept of a field.
Basics of vector calculus: gradient, line, surface and volume integrals, curl and Stokes' theorem, divergence and Gauss' theorem.
Sources and vortices of a field, Helmholtz's theorem.

Electrostatics (12 hours)

Electric charge, Coulomb's law, and the Superposition Principle.
Electrostatic field E in vacuum. Divergence and curl of E (differential formulation). Gauss' and Stokes' theorems (integral formulation).
Electrostatic potential, Poisson's and Laplace's equations.
Multipole expansion of the electrostatic potential (optional).
Electrostatic energy.

Electrostatic Field in Matter (10 hours)

Definition of conductors and insulators.
Conductors in an electrostatic field.
Force on surface charge and electrostatic pressure (brief overview).
Electric capacitance and capacitors.
General electrostatic problem in the presence of conductors: study of Laplace’s equation. Method of image charges (optional).
Dielectrics. Induced and permanent atomic and molecular dipoles. Electric polarization. Field of a polarized dielectric. Polarization charges.
Electric displacement field D. Sources and vortices of D. Discontinuities in E and D fields.
Electric susceptibility, permittivity, and dielectric constant. Linear dielectrics.
Electrostatic energy in dielectric systems.

Steady Electric Current (6 hours)

Moving charges and electric current.
Current density vector.
Charge conservation and general continuity equation.
Ohmic conductors.
Electromotive force.
Joule heating.
Overview of resistor networks.

Steady Magnetic Field (10 hours)

Biot-Savart law and magnetic field B in vacuum.
Sources and vortices of magnetic field B: divergence and curl of B.
Ampère's law.
Vector potential A and boundary conditions in magnetostatics.
Multipole expansion of the vector potential (optional).
Magnetic field B in matter. Magnetic dipoles and magnetization. Field of a magnetized object and magnetization currents.
Magnetic field H. Sources and vortices of H and discontinuities in B and H fields.
Diamagnetism, paramagnetism, and ferromagnetism.
Linear and nonlinear media: magnetic susceptibility and permeability (optional).

The Electromagnetic Field in Time-Varying Conditions (6 hours)

Sources of electromotive force and induced electromotive force.
Faraday's law and Lenz's law.
Mutual induction and self-induction.
Overview of time-varying current circuits.
Magnetic energy.

Maxwell’s Equations (6 hours)

Displacement current and symmetries in electromagnetism equations.
Maxwell’s equations and the problem of magnetic monopoles.
Overview of Maxwell’s equations in matter: boundary conditions for E, B, D, and H fields.
Formulation of electrodynamics in terms of potentials and gauge transformations (Coulomb and Lorenz gauges), Lorentz force in terms of potentials (optional).
Energy conservation and Poynting's theorem.
Solutions to Maxwell's equations in vacuum and in the absence of charges and currents: electromagnetic waves. 

Readings/Bibliography

Any university-level textbook on Electromagnetism is suitable for the course. It is strongly recommended to study the topics using a textbook, in addition to class notes and the materials available on the institutional platform virtuale.unibo.it [https://virtuale.unibo.it], where all exercises proposed during the lectures are also provided.

Practice exercises to assess your level of preparation can also be found on virtuale.unibo.it [https://virtuale.unibo.it] .

For students who did not attend the course, it is recommended to use the syllabus and materials available on virtuale.unibo.it [https://virtuale.unibo.it] to prepare for the exam.

Below is a list of recommended textbooks:

  • S. Focardi, I. Massa e A. Uguzzoni: Fisica Generale - Elettromagnetismo, Casa Editrice Ambrosiana;
  • C. Mencuccini, A. Silvestrini: Fisica II - Liguori Editore (capitoli I-VII e IX);
  • P. Mazzoldi, M. Nigro, C. Voci: Elementi di Fisica - Elettromagnetismo e Onde - Casa editrice EdiSES (capitoli 1-10);
  • Giancoli: Fisica 2, Casa Editrice Ambrosiana (capitoli 21-31);
  • Resnik, Holliday, Krane: Fisica 2 - Casa Editrice Ambrosiana;

Teaching methods

The course takes place in the second term and is a continuation of the General Physics T-1 course. Therefore, a solid understanding of General Physics T-1, as well as Calculus I and II, is recommended.

The General Physics T-2 course consists of in-person lectures. In addition to theoretical aspects, exercises are also proposed to help students prepare for the final assessment.

Attendance is strongly recommended as it supports the learning process of concepts and notions. However, it does not directly affect the final grade.

Assessment methods

The final assessment consists of a two-hour written exam followed by an oral exam lasting up to thirty minutes.

During the written exam, students are required to solve a number of open-ended problems (with numerical or symbolic answers) on topics covered in the course. The use of books, notes, electronic devices, and mobile phones is not permitted during the exam. If the result of the written exam is deemed satisfactory (equal to or greater than 18/30), it remains valid for the entire exam session.

To access the oral exam, students must have obtained a grade of at least 18/30 on the written exam. The oral exam begins with a review of the written paper and continues with a discussion on topics from the course.

The final grade is a weighted average of the written and oral exam results. Students have the option to reject the proposed grade and choose to retake the exam (either just the oral or both parts).

The exam schedule is published well in advance on the instructor’s official webpage [https://www.unibo.it/sitoweb/elena.cuoco/didattica ] and on AlmaEsami [https://almaesami.unibo.it/almaesami/welcome.htm ].

Students wishing to take the exam must register on the appropriate exam list (for both the written and oral parts) via AlmaEsami [https://almaesami.unibo.it/almaesami/welcome.htm ].

Please remember to always bring a valid ID.

Teaching tools

On the virtuale.unibo.it [https://virtuale.unibo.it] platform, you can find the exercises proposed during the lectures as well as past exam papers with solutions. The topics covered in the course are also listed, along with some interesting insights related to electromagnetism.

Students with specific learning disorders (SLD) or temporary/permanent disabilities:

We recommend contacting the University Office responsible for support services in a timely manner (https://site.unibo.it/studenti-con-disabilita-e-dsa/it) [https://site.unibo.it/studenti-con-disabilita-e-dsa/it):] ). The office will evaluate the students' needs and, where appropriate, propose possible accommodations. These must in any case be submitted for approval at least 15 days in advance to the course instructor, who will assess their suitability also in relation to the learning objectives of the course.

Office hours

See the website of Elena Cuoco