Electrostatic fields form the basis for such everyday applications as air cleaners, photocopiers, spark plugs, and corona discharges, to name a few. In this chapter we will explore several techniques that can be used to determine the electric field produced by a single electric charge, or a distribution of electric charges, including two fundamental relations known as Coulomb’s Law and Gauss’ Law. Gauss’ Law is one of two differential properties obeyed by electric fields that we will explore. We will show that the electric field can be determined from an electric potential, and explore methods of determining the electric potential. Using the electric potential can often be a simpler approach for finding the electric field. We will then examine the influence of materials, including conductors and dielectrics (or insulators), on electric fields. This will require us to re-examine Gauss’ Law to include material effects. We will also develop a set of relations, known as boundary conditions, that relate the fields on the two sides of an interface between two materials. Our studies begin with empirical observations of the force between two charged bodies.

This project involves the application of molecular dynamics (MD) to a simple two-dimensional planetary system consisting of two planets and a fixed star. The primary focus is to construct a MD code using Newton’s law of universal gravitation as the interaction law and the Verlet algorithm for solving the initial value problem. The project examines the gravitational interaction described by Newton’s laws, focusing on the law of universal gravitation and its application to the planetary system. It further explores the principle of equivalence, the concept of conservative force, and the effective potential energy of the system. The discussion also covers the reduction of a single planet motion to one dimension, which offers insights into the trajectory of the planetary system. Finally, the project outlines the numerical approach using the Verlet algorithm for simulating the motion of the planets. The comprehensive understanding of the gravitational interactions and the computational techniques provide a solid foundation for the study of complex dynamical systems.