This chapter presents a comprehensive exploration of methods and concepts in electrostatics and electrodynamics, focusing on three primary techniques: the separation of variables, the method of images and the Finite Element Analysis for two-dimensional cases. The method of images is introduced as a powerful tool for solving boundary problems by strategically placing imaginary charges outside the region of interest to satisfy boundary conditions. Detailed derivations are provided for the potential, electric field, surface charge density, Coulomb force and the work required to move charges in various configurations. A significant portion of the chapter is devoted to understanding the interaction between a point charge and a grounded conducting sphere. This analysis includes deriving the potential and force due to image charges, as well as examining special cases where the force approximates Coulomb’s law at short distances and deviates at long distances. The induced surface charge density on the sphere is also derived and analyzed for different angular positions. Further, the interaction between a point charge and an insulated conducting sphere is explored, incorporating the superposition principle to determine the resulting potential and forces. The behaviour of a conducting sphere in a uniform electric field is also examined, highlighting how image charges satisfy boundary conditions and how the induced surface charge density varies across the sphere’s surface. The chapter extends to advanced topics such as multipole expansion, which is used to describe the electric potential of complex charge distributions. This includes the monopole, dipole and quadrupole contributions, with particular emphasis on the behaviour of these potentials at large distances. The concept of vector potential is introduced, using multipole moments to analyze magnetic fields and the magnetic dipole moment, emphasizing its consistency with Maxwell’s equations. Theoretical developments are complemented by applications that include the calculation of potentials, forces and surface charge densities for dipoles and quadrupoles, as well as the analysis of magnetic field configurations. To reinforce the concepts, the chapter includes solved examples and unsolved problems that encourage further exploration and practical application of the principles discussed.