Electrodynamics: In-depth Solutions for Maxwell’s Equations

Overview

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This course is the fourth course in the Electrodynamics series, and is directly proceeded by Electrodynamics: Electric and Magnetic Fields. Previously, we have learned about visualization of fields and solutions which were not time dependent. Here, we will return to Maxwell's Equations and use them to produce wave equations which can be used to analyze complex systems, such as oscillating dipoles. We will also introduce AC circuits, and how they can be simplified, solved, and applied. Learners will: • Have a complete understanding of Maxwell's Equations and how they relate to the magnetic and electric potentials. • Be able to solve problems related to moving charges, and add relativistic corrections to the equations • Understand the different components in AC circuits, and how their presence can change the function of the circuit. The approach taken in this course complements traditional approaches, covering a fairly complete treatment of the physics of electricity and magnetism, and adds Feynman’s unique and vital approach to grasping a picture of the physical universe. Furthermore, this course uniquely provides the link between the knowledge of electrodynamics and its practical applications to research in materials science, information technology, electrical engineering, chemistry, chemical engineering, energy storage, energy harvesting, and other materials related fields.

Syllabus

The Laws of Induction

This lecture will cover the concept of flux, EMF, and inductance. We will start by describing how the EMF is produced, how it can affect other units, and its different applications. Then, the relationship between coils of wire is described using mutual inductance, and the effect of a wire on itself is discussed in terms of self-inductance.

The Maxwell Equations

In previous lectures, we have been working with a simple version of Maxwell’s 4th equation. In this lecture, we will discuss the more complete form, and all of the equations necessary to describe classical physics. Furthermore, we will start to analyze the concept of traveling fields, which propagate free from their source. Finally, we will present the wave equation for the magnetic and electric potentials.

Maxwell's Equations in Free Space

Continuing from the previous lecture, we will discuss traveling waves in greater detail. We will expand on the wave equation by showing how both Electric and Magnetic fields also can be modeled by the 3-D wave equation. Furthermore, we will distinguish between how spherical and one-dimensional fields travel.

Maxwell's Equations with Currents and Charges

In this lecture, we delve into deeply into relativistic and time-dependent solutions. To do this, we show how different equations can be corrected to account for position changes. We will expand on situations from previous lectures, and show how the equations modeling them will change if they are time-dependent. Finally we will discuss how Maxwell’s equations lead to the Lorentz transformation.

Introduction to Alternating Circuits

Throughout this course, we have mostly analyzed charges or independent units of circuits. In this lecture, we will discuss the basics of analyzing full circuits, which assuming most situations are ideal. To do this, the concept of impedance will be introduced, along with techniques to solve and simplify an entire circuit.