Problems in Classical Electromagnetism

Abstract

This book comprises 157 problems in classical electromagnetism, originating from the second-year course given by the authors to the undergraduate students of physics at the University of Pisa in the years from 2002 to 2017. Our course covers the basics of classical electromagnetism in a fairly complete way. In the first part, we present electrostatics and magnetostatics, electric currents, and magnetic induction, introducing the complete set of Maxwell’s equations. The second part is devoted to the conservation properties of Maxwell’s equations, the classical theory of radiation, the relativistic transformation of the fields, and the propagation of electromagnetic waves in matter or along transmission lines and waveguides. Typically, the total amount of lectures and exercise classes is about 90 and 45 hours, respectively. Most of the problems of this book were prepared for the intermediate and final examinations. In an examination test, a student is requested to solve two or three problems in 3 hours. The more complex problems are presented and discussed in detail during the classes. The prerequisite for tackling these problems is having successfully passed the first year of undergraduate studies in physics, mathematics, or engineering, acquiring a good knowledge of elementary classical mechanics, linear algebra, differential calculus for functions of one variable. Obviously, classical electromagnetism requires differential calculus involving functions of more than one variable. This, in our undergraduate programme, is taught in parallel courses of the second year. Typically, however, the basic concepts needed to write down the Maxwell equations in differential form are introduced and discussed in our electromagnetism course, in the simplest possible way. Actually, while we do not require higher mathematical methods as a prerequisite, the electromagnetism course is probably the place where the students will encounter for the first time topics such as Fourier series and transform, at least in a heuristic way.