Electrodynamics: In-depth Solutions for Maxwell’s Equations

Go to Course: https://www.coursera.org/learn/electrodynamics-solutions-maxwells-equations

Introduction

## Course Review: Electrodynamics: In-depth Solutions for Maxwell’s Equations If you are looking to deepen your understanding of electromagnetism and its practical applications, the Coursera course "Electrodynamics: In-depth Solutions for Maxwell’s Equations" is a remarkable opportunity. As the fourth course in the specialized Electrodynamics series, this course offers an insightful dive into complex systems governed by Maxwell’s equations, including wave phenomena and alternating current circuits. ### Course Overview This course builds upon your knowledge from earlier courses in the Electrodynamics series, particularly "Electrodynamics: Electric and Magnetic Fields." You will revisit Maxwell's equations and use them to derive wave equations applicable in analyzing dynamic systems such as oscillating dipoles. With a focus on both theoretical principles and their real-world implications, you’ll be equipped to understand modern technology that relies heavily on these foundational physical concepts. ### Detailed Syllabus The course is structured systematically, allowing learners to build expertise progressively. Let's break down the core modules: 1. **The Laws of Induction** - This module introduces key concepts like flux, electromotive force (EMF), and inductance. The detailed explanations of self-inductance and mutual inductance set the stage for understanding how electromagnetic fields interact. 2. **The Maxwell Equations** - You will explore the complete form of Maxwell's equations, moving beyond simplified versions. This deep dive allows you to comprehend traveling fields free from their sources, culminating in a practical understanding of electric and magnetic potentials. 3. **Maxwell's Equations in Free Space** - This lecture expands on the wave equation, helping you model electric and magnetic fields using the three-dimensional wave equation. You'll differentiate how spherical and one-dimensional waves propagate, enhancing your grasp of electromagnetic behavior. 4. **Maxwell's Equations with Currents and Charges** - Delving into relativistic and time-dependent solutions, this module encourages learners to consider equations under variable conditions. The introduction of the Lorentz transformation enriches your understanding of electromagnetic fields in different reference frames. 5. **Introduction to Alternating Circuits** - Here, you'll transition from isolated charges to analyzing complete circuits. The addition of impedance and techniques for simplifying circuits are crucial for those interested in electronics. 6. **Final Project** - The course culminates in a practical project that allows you to apply your learning. This hands-on experience reinforces your understanding by enabling you to tackle complex problems. ### Course Experience The structure of the course caters to both theoretical understanding and practical application. Each lecture is thoughtfully crafted, balancing in-depth explanations with engaging visuals that enhance comprehension. The instructors are knowledgeable and adept at breaking down complex topics into manageable lessons. Their passion for the subject matter is evident and motivating for students. ### Target Audience This course is ideal for advanced learners in physics or electrical engineering, particularly those who have completed introductory courses in electrodynamics. If you have a keen interest in the theoretical foundations that underpin much of modern technology, this course will be particularly beneficial. ### Recommendation I wholeheartedly recommend "Electrodynamics: In-depth Solutions for Maxwell’s Equations" for anyone looking to gain a comprehensive understanding of electromagnetism. The course not only provides substantial theoretical knowledge but also emphasizes the application of that knowledge in real-world scenarios. By the end of the course, learners can expect to enhance their problem-solving skills and expand their competence in analyzing electromagnetic systems. Whether you're a student, a professional in the field, or simply curious about electrodynamics, this course promises to be a valuable addition to your educational journey.

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.

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.

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.

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.

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.