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Electrodynamics: An Introduction

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  • Introduction and Basics of Electrostatics
    • In this module, electrodynamics is introduced by examining the different forces and explaining which are related to electric forces. Furthermore, fields are defined and we differentiate between scalar and vector fields. We cover laws that constitute electrodynamics, specifically Maxwell's equations and the Lorentz force. After explaining how these topics can be illustrated, we also cover how relativity relates to the subject material.
  • Introduction to Differential Calculus of Vector Fields
    • This module mainly covers the mathematics behind differential forms of equations. We introduce the ∇ operator and show how it can be used in mathematics. Then, the ∇ operator is proved to be a vector. The Maxwell equations are rewritten in derivative form, and the concepts of divergence and curl are introduced. Finally, we examine the Laplace operator, and other forms of the ∇ operator applied twice.
  • Introduction to Vector Integral Calculus
    • This module explains line integrals and presents some equations where they are important. We explain what the flux and circulation of a field are conceptually and how they can be obtain using the divergence and curl through Gauss' and Stokes' theorems respectively. Finally, we explain the qualities of divergence and curl free fields.
  • Introduction to Electrostatic Solutions
    • This module covers how to simplify Maxwell's equations in the scenario of electrostatics. Then, we discuss how the electric potential can be used and why using a relative value is useful for certain calculations. The flux out of different geometries is presented, as well as how to display field lines and equipotential surfaces.
  • The Application of Gauss' Law
    • This module focusses primarily on electric fields. First, we talk about the mathematical requirements for equilibrium and the implications of finding equilibrium for point charges. Then we move on to describe the electric field coming from different geometries. Finally, we compare the electric fields inside and outside of a conductor and how they create the phenomenon of electric shielding.