30547 - FOUNDATIONS OF PHYSICS II
Course taught in English
Go to class group/s: 27
For a deep and effective learning experience, it is recommended a preliminary knowledge of: - multivariable calculus (limits, partial derivatives, line and surface integrals), vector spaces, linear algebra and differential equations. - Mechanics Basic Course (force, energy, torque, particle and rigid body motion, basic understanding of the concept of wave).
Electromagnetism is a fundamental part of physics with considerable technological applications, ranging from computer devices to signal processing. The laws of electromagnetism are written in terms of advanced mathematical concepts (ranging from calculus to topology, to wave equations) and constitute a challenging conceptual framework in which advanced modelling technique and mathematics make contact.
Mathematical introduction: scalar and vector fields. Divergence and curl and their geometrical meaning. Laplacian. Divergence and Stokes' theorem. Dirac delta function.
Electrostatics in vacuum: electric charge, Coulombs law, superposition principle, electric fields and Gauss's law. Electric potential. Electric dipole. Work and energy of charged particles.
Conductors: Electrostatic induction. Screening and Faraday cage. Capacitors. Laplace's and Poisson's equations.
Electric fields inside matter: dielectrics, polarization. Electric current and the theory of circuits. Ohm’s law, Kirchhoff's circuit laws. Joule's law. Electromotive force (EMF), charging and discharging of capacitors, circuit analysis.
Magnetostatics in vacuum: Lorentz force. Biot-Savart law. Magnetic moment. Properties of the magnetic field in the stationary case: the divergence of the magnetic field and Ampere's law.
Magnetic fields inside matter: magnetic polarisation and an overview of magnetic materials; diamagnets, paramagnets, ferromagnets.
Electromagnetic induction: Faraday-Lenz law. Inductance. LR circuits. Energy of the magnetic field. Mutual inductance.
Maxwell's equations: wave equation, velocity of light, wave propagation.
Know the most advanced laws of classical physics, expressed both in integral and in differential forms.
Understand how advanced mathematical concepts play a role in their definition (line and surface integrals, topology, differential equations)
Understand wave propagation
Make connections between electromagnetism and special relativity.
- Performing calculations of electric and magnetic fields in space in some selected geometries with boundary conditions.
- Performing calculations of stationary and time-dependent electrical currents in circuits.
- Account for basic theories in electrostatics and magnetostatics, electrical circuits, stationary electromagnetism and electromagnetic induction.
- Study wave propagation in simple settings
- Face-to-face lectures
- Exercises (exercises, database, software etc.)
Exercise sessions are dedicated to problem solving using advanced mathematical tools.
|Continuous assessment||Partial exams||General exam|
Students will be evaluated on the basis of written exams and a group project. The written exam will be divided into two partial exams held during the semester or one final general exam.
Each type of exam will contribute to the final grade as follows:
Genera written: 32 points
Each written partial: 16 points
A grade of 30 cum laude corresponds to 31 or 32 points.
To pass the exam, students must earn a grade of at least 18.
The written exams consists in solving some exercises to be worked out on paper. The purpose of the exercises will be to test knowledge of fundamental physical laws and the ability to model and solve problems. An aptitude for problem solving along with a rigorous use of advanced mathematical tools is the main skill the exams are intended to assess. The written exam is not be open-book.
The recommended textbook is:
- David J. Griffiths - Introduction to Electrodynamics, 4th ed., (2012). Addison-Wesley. ISBN 978-0-321-85656-2.
Additional lecture notes will be provided then content of the lectures deviates from the book.
The book contains for each chapter many exercises whose solutions can be found in:
- David J. Griffiths (2014) Instructor’s Solution Manual Introduction to Electrodynamics, Fourth Edition.
For further study, clarification and (solved) exercises, please consult:
- Edward M. Purcell, David J. Morin - Electricity and Magnetism, 3d ed., (2013). Cambridge University Press.
- David Halliday, Robert Resnick, Jearl Walker - Fundamentals of Physics, (2018). Extended-Wiley