Electrical Engineering

Introduction to Electromagnetism Maxwell's postulates and equations in differential form. Constitutive relationships. Boundary conditions. Maxwell's equations in integral form. Dirac delta. Static fields Decoupling of electric and magnetic fields. Static balance and conductors. Stationary currents. Reminder of Electrostatics Gauss' law and applications. electrostatic potential. Boundary conditions for the electrostatic field. Uniqueness of the solution of the electrostatic problem. Poisson equations and Laplace equation. Laplace's equation Sturm-Liouville problems: eigenvalues and eigenfunctions. Orthogonality and uniqueness of eigenfunctions. Development in eigenfunctions. Fourier series. The method of separation of variables. Solution of the Laplace equation for bodies under an external field. Boundary value problems in rectangular coordinates Laplace's equation in rectangular coordinates. Sturm-Liouville problem for the harmonic differential equation. Orthogonal eigenfunction systems: trigonometric functions. Applications. Boundary value problems in cylindrical coordinates Laplace's equation in cylindrical coordinates. Sturm-Liouville problem for the Bessel differential equation. Orthogonal eigenfunction systems: the Bessel functions. Applications. Boundary value problems in spherical coordinates Laplace's equation in spherical coordinates. Sturm-Liouville problem for the Legendre differential equation. Orthogonal eigenfunction systems: Legendre functions and polynomials. Applications. Poisson's equation Uniqueness of the solution of the Poisson equation. Green's function method. The three-dimensional static Green's function of free space. Coulomb's law. The two-dimensional static Green's function of free space. Dirichlet's and Neumann's Green's functions. Image method. Applications. Spherical harmonics. Potential development of a point charge. Multipole development. The Fourier transform. The Fourier-Bessel transform. Green's function via Fourier transform. Problems with stratified media. Introduction to Magnetostatics Magnetostatic field equations. Ampere's law. The scalar magnetic potential. The magnetic vector potential. Integral solution for the vector potential.

Students are expected to be familiar with some basic concepts of algebra, geometry and mathematical analysis. In particular, before tackling the course it is advisable to review vector algebra, differential calculus (derivatives, gradient, divergence, curl, Laplacian), integral calculus (line integrals, surface integrals, volume integrals) and systems of curvilinear coordinates (rectangular, cylindrical, spherical), as well as the solution of ordinary differential equations of the second order with constant coefficients. It would be advisable to have passed the exams of Mathematical Analysis 1, Mathematical Analysis 2, Physics 1, Physics 2, Electrotechnics 1.

J. D. Jackson, Classical Electrodymanics, 3a ed., Wiley, 1999. D. J. Griffiths, Introduction to Electrodynamics, 4a ed., PHI Learning, 2017.

Attendance is not compulsory, but recommended in order to be able to follow the contents of the course with continuity.

The examination consists either in one question about part of the contents of the course or in the solution/discussion of an excercise. The purpose of the examination is to verify that the student has acquired the analytical techniques illustrated in the course and knows how to apply them to elementary problems. The result of the exam will be "pass" or "fail".

J. A. Edminister, "Elettromagnetismo", McGraw-Hill Education, 1994. W. R. Smythe, "Static and Dynamic Electricity", CRC Press, 1989. J. H. Jeans, "Mathematical Theory of Electricity and Magnetism", 5a ed., CUP, 1958. E. Durand, "Electrostatique et Magnétostatique", Masson, 1953.

The course will take place through 15 video lessons (lasting 2 hours each), in order to allow maximum usability of the course even by students who cannot for work reasons and/or concurrent lessons of other courses. The video lessons are prepared by the teacher through self-consistent slides which are always available on the course web page.