ABSTRACT
To understand the basic principles of magnets, gradient coils, and radiofrequency resonators used in magnetic resonance imaging, we must first understand basic electromagnetic theory. This chapter reviews some basic concepts and formulae of vector analysis. It also reviews the basic theory of static magnetic fields and time-harmonic electromagnetic fields. These include Helmholtz and Maxwell coils, inductance calculations, and the magnetic fields produced by some special cylindrical and spherical surface that form the foundation for birdcage coil and magnet designs. The most useful concepts in vector analysis are those of divergence, curl, and gradient. The chapter presents the definitions for the quantities and the related theorems. It provides the general solution of the magnetic field in source-free regions in cylindrical and spherical coordinates. The chapter also provides a discussion on the boundary conditions for magnetostatic fields across a current sheet in free space, which are useful in finding the magnetic fields produced by planar, cylindrical, and spherical surface currents.
