Maxwell's Four Equations That Changed Everything (Explained Without Numbers)

This past spring semester, when a faculty member had to take an unexpected leave at the 5th week of a 15 week semester, I picked up an Electromagnetic Fields and Waves course at The University of Hartford. It is one of the most difficult courses in an Electrical Engineering program with some pretty heavy math. While it is still fresh, here's a no-math explanation of Maxwell’s equation set, the fundamental principles underlying nearly all contemporary electrical engineering and technology.....

In the 1860s, James Clerk Maxwell identified four equations that unified electricity and magnetism into a single electromagnetic theory. These mathematical expressions revealed how electric and magnetic fields interact and generate each other, providing a framework for understanding electromagnetic phenomena throughout the universe.

Equation 1: Gauss's Law for Electricity 

Electric charges produce electric fields which surround them. For example, the electric field generated by a charged balloon when close, causes your hair to stand up. That charge extends through all directions and as the amount of charge increases, a stronger electric field is produced.

Equation 2: Gauss's Law for Magnetism 

The fundamental principle revealed by Gauss's Law for Magnetism demonstrates that magnetic monopoles do not exist. Electric charges exist independently as positive or negative entities but magnets exist only as dual poles that include north and south magnetic ends. For example, cutting a magnet into two pieces produces two smaller magnets that each contain both north and south poles. 

Equation 3: Faraday's Law 

The relationship between shifting magnetic fields and electric field generation is defined through Faraday's Law. The operation of power plant generators depends on this fundamental principle. A magnet will generate electricity when it moves through a coil of wire because the altering magnetic field produces electric current. For example, you may remember from a high school science experiment that passing a magnet through a copper coil can result in enough electric current flow to light up a lightbulb.

Equation 4: Ampère's Law with Maxwell's Modification 

Flipping things around, Equations 4 identifies an opposite process, demonstrating how electric currents together with changing electric fields produce magnetic fields. For example, the movement of electric current through wires produces magnetic field deflection that enables the operation of doorbell systems, MRI machines, and those giant electromagnets you see used on cranes in junkyards.

Together, these four equations show that electric and magnetic fields are interconnected - they can transform into each other and propagate through space as electromagnetic waves, including light, radio waves, and X-rays. They form the theoretical foundation for virtually all modern electrical technology.

Some Of My Favorite AI Tools For Engineering Students

As an engineering professor, I've seen how AI tools are transforming how we tackle our coursework, from solving complex equations and debugging code to creating visualizations and polishing lab reports. Whether you are wrestling with thermodynamics problems at midnight or designing circuits for a project, these AI assistants will help you work smarter and learn more effectively. Here's a list of some of my favorite AI enabled resources for engineering students. This list is in no way complete!

 

For Problem-Solving and Calculations:

·       Wolfram Alpha - Exceptional for advanced mathematics, physics, and engineering calculations. It can solve differential equations, perform matrix operations, and provide step-by-step solutions.

·       Symbolab - Great for calculus, linear algebra, and showing detailed problem-solving steps.

·       MATLAB Online - While not purely AI, it includes AI/ML toolboxes and is essential for many engineering courses. We all use it!

 

For Research and Learning:

·       Claude - Helpful for explaining complex engineering concepts, debugging code, and providing detailed technical explanations.

·       Gemini (Google's AI) - Excellent for research and technical explanations, with strong integration with Google services and ability to analyze images and technical diagrams.

·       ChatGPT - Good for general engineering questions and concept clarification.

·       Perplexity AI - Excellent for research as it provides citations and up-to-date information.

 

For Programming and Code:

·       GitHub Copilot - Invaluable for coding assignments in Python, C++, MATLAB, and other languages commonly used in engineering.

·       Replit AI - Integrated coding environment with AI assistance.

·       Gemini Code Assist - Google's coding assistant, particularly strong with Google Cloud and web development.

 

For Design and Visualization:

·       DALL-E 3 or Midjourney - Useful for creating diagrams, conceptual designs, or visualizations for presentations.

·       Canva AI - Helpful for creating professional presentations and posters.

 

For Writing and Documentation:

·       Grammarly - Essential for lab reports, technical writing, and documentation.

·       Quillbot - Useful for paraphrasing and improving technical writing clarity.

 

Specialized Engineering Tools:

·       Ansys AI - For simulation and analysis in mechanical/aerospace engineering.

·       PSpice - Industry-standard circuit simulation software .

·       CircuitLab - For electrical engineering circuit analysis.

 

Study and Organization:

·       Notion AI - Great for organizing notes, creating study guides, and managing projects.

·       Anki with AI plugins - For creating smart flashcards for technical terms and formulas.

 

These are just some of many excellent AI tools that I use.... some are more "AI" than others. Most colleges and universities offer free or discounted access to many of these tools. I'd recommend starting with one or two that match your immediate needs and gradually exploring others as you progress through your coursework. Always check your university's academic integrity policies regarding AI use in assignments.

A Response - Rethinking Engineering Education for the AI Era

In my last post, Reimagining Engineering Homework with Simulators in the Age of AI, I argued that traditional electrical engineering homework focused on calculations is now easily solved by AI, requiring educators to shift to simulator-based assignments that develop higher-order skills like design, troubleshooting, and systems thinking. By using circuit simulation tools, students can engage in active experimentation and real-world problem-solving that requires distinctly human engineering judgment that AI cannot replicate.

I received the following comment on the post: 

I agree that it makes no sense to assess students' ability to make calculations that the simulators they are familiar with already make. The problem, though, is that even the tasks you suggest (e.g., create a design that meets specifications) can be already be accomplished by a variety of generative artificial intelligence platforms. Which begs the questions: what will the electrical engineers we are training actually do when they graduate, and what will they need to know in order to do it?

I’d be a liar if I said I was not asking myself the same questions. Here’s my reply:

You raise a crucial point that goes to the heart of modern engineering education. The rapid advancement of AI tools that can handle both calculations and design tasks challenges us to fundamentally reconsider what students need to learn.

I think the key lies in developing capabilities that remain distinctly human, even as AI handles more routine tasks. Future electrical engineers will likely need to excel in:

Systems thinking and integration - While AI can generate designs meeting specific parameters, engineers must understand how components interact within larger systems, identify trade-offs, and make judgment calls that balance competing constraints beyond what can be easily quantified.

Problem definition and formulation - Perhaps most critically, engineers need to determine what problems to solve in the first place. AI can optimize solutions, but it still requires human insight to identify the right questions and define meaningful specifications that serve real human needs.

Critical evaluation and verification - Engineers must be able to assess AI-generated solutions, spot errors or limitations, and validate that designs work in real-world conditions with all their messy complexities.

Innovation at the intersection - The most valuable engineers will combine domain expertise with an understanding of what AI can and cannot do, using these tools creatively to solve problems that neither humans nor AI could tackle alone.

Rather than competing with AI on tasks it can already do, engineering education must focus on these higher-level skills while using AI tools as aids in the learning process itself. 

Reimagining Engineering Homework with Simulators in the Age of AI

…. simulator-based assignments shift engineering education from passive computation to active

investigation…..

As AI tools now easily solve most traditional homework problems, engineering educators face a critical inflection point in meaningful assignment design. In my discipline, electrical engineering, the traditional homework model, focused on calculating impedance, solving differential equations, or applying Kirchhoff's laws, no longer serves as an effective assessment of student understanding. Fortunately, circuit simulation technologies offer a powerful supplement that transforms how students engage with electrical engineering concepts.

Simulators like PSpice, Multisim, and MATLAB provide virtual laboratories where students can experiment without physical constraints. Rather than simply calculating a circuit's frequency response, students can manipulate component values, sweep frequencies, and observe real-time effects through virtual oscilloscopes and spectrum analyzers. This shifts homework from passive computation to active investigation. When a student asks "what happens if I replace this capacitor?" they're engaging in authentic engineering inquiry that AI (at least not yet) cannot replicate.

The educational value extends beyond mere observation. Quality circuit simulator-based assignments require students to predict behavior, troubleshoot unexpected results, and optimize designs within real-world constraints. Students might investigate why their amplifier circuit distorts at specific frequencies, determine the optimal filter topology for a given application, or debug timing issues in a digital logic system. These higher-order engineering thinking skills remain distinctly human despite AI's computational prowess.

Virtual circuit simulators democratize access to sophisticated equipment and scenarios that might otherwise be unavailable due to cost, safety concerns, or physical limitations. Consider electrical engineering students without access to $10,000 oscilloscopes, spectrum analyzers, or signal generators, through simulators they can conduct virtual experiments with professional grade virtual instrumentation. Students can work with high voltage power electronics without risk of electrocution, or experiment with expensive radio frequency components without fear of destroying them. Those with mobility limitations gain equitable access to bench electronics through virtual labs requiring no physical soldering or manipulation of components.

The boundaries of practical learning dissolve as well. Students can simulate microwave circuits operating at 77 GHz for automotive radar, design integrated circuits with nanometer-scale transistors, or test power distribution networks for satellite systems, applications that would be physically inaccessible due to fabrication requirements or specialized equipment needs. Time constraints also vanish: simulations can compress hours of thermal analysis into seconds, or slow down switching transients in power converters to observable speeds. This temporal flexibility enables understanding of electrical phenomena that operate on timescales incompatible with traditional oscilloscope measurements.

Perhaps most importantly, simulators create a psychological safety net that encourages bold experimentation. Students can intentionally exceed component ratings, create short circuits, or test failure modes without destroying expensive components or creating safety hazards. They can iterate rapidly through dozens of design variations without the time consuming process of physically rebuilding circuits. This freedom to fail productively cultivates the innovative thinking critical for solving complex electrical engineering problems that AI cannot address.

Applications will further develop collaboration features for circuit simulation platforms, creating environments that mirror real electrical engineering workplaces. Students will share designs, conduct peer reviews, and tackle complex projects like software defined radios together. This approach teaches essential professional skills including communicating design intentions, resolving different specification approaches, and building consensus, social learning experiences that AI tools cannot replicate.

For electrical engineering educators, the transition requires rethinking assessment metrics. Rather than evaluating whether a student correctly calculated a circuit's gain, we must develop rubrics that measure design robustness, component selection rationale, and troubleshooting methodology. The focus shifts from "did they get the right transfer function?" to "did they create a design that meets specifications under varied conditions?"

 

Pspice Lab Series Video 3: Moving The Reference Ground Around

Zero volts reference, also known as ground is always a confusing topic. What if ground is placed at different locations in a circuit? In this 11 minute and 42 second video I use PSpice to show what happens when you move a ground around in a series circuit.

Want to learn more? I’ll be teaching a Systems 1 course online in the fall and a Systems 2 course in the spring at Holyoke Community College. If you are anywhere in the world and interested in taking an online course with me drop an email to gsnyder@hcc.edu Both courses will transfer to most university electrical engineering programs in the United States. Hope to see you there!!

Pspice Lab Series Video 2: Simple Series Resistive Circuits

 Here's a second PSPice video covering analysis of a simple series circuit with two dc voltage sources and four resistors.

Want to learn more? I’ll be teaching a Systems 1 course online in the fall and a Systems 2 course in the spring at Holyoke Community College. If you are anywhere in the world and interested in taking an online course with me drop an email to gsnyder@hcc.edu Both courses will transfer to most university electrical engineering programs in the United States. Hope to see you there!!

PSpice Lab Series Video 1

Over the summer I’ll be working on a series of OrCAD PSpice videos. PSpice is one of the most common analog and mixed signal circuit simulator and verification tools used by electrical engineers to rapidly move through the design cycle, from circuit exploration to design development and verification. It is also a lot of fun to play around with!

I’m developing a series of 25-30 online experiments that we’ll be using in my EGR223 - System Analysis (Circuit Analysis 1) and EGR 224 - System Analysis (Circuit Analysis 2) courses at Holyoke Community College. Here’s the first video in the series.

OrCAD has an excellent academic program that provides students and educators with a complete suite of design and analysis tools to learn, teach, and create electronic hardware. If you are a student or educator you can download the software here for free and follow along with my labs. If you are not a student or educator (or perhaps considering) you can download and install a trial version of the software here.

I’ll be teaching the Systems 1 course online in the fall and the Systems 2 course at Holyoke Community College in the spring so if you are anywhere in the world and interested in taking a course with me drop an email to gsnyder@hcc.edu Both courses will transfer to most university electrical engineering programs in the United States. Hope to see you there!!

Tektronix Oscilloscope Tutorials

I came into Electrical Engineering a different way than most - starting as a graduate student with an undergraduate degree in Microbiology. These two disciplines are slightly different - Microbiologists use microscopes and EE's use oscilloscopes :) I knew I had some catching up to do and remember one of my major goals for the summer before I started grad school was to learn how to use an oscilloscope. Fortunately I came across a free tutorial booklet from Tektronix on understanding and using an oscilloscope which made it pretty easy.

Well, even though that was over 30 years ago now, the Tektronix free tutorial materials still exist and they are even better than before. If you are starting from scratch or just want to brush up these are highly recommended. Here's a link to the tutorial page. Good stuff!

Curiosity on Mars Bringing Back Memories

The Mars landing of Curiosity has brought back some memories when it comes to sensors and systems in space.....

It was 1980. I was a year out of college with an undergrad degree in microbiology and working in a hospital lab trying to figure out what I wanted to do for the rest of my life. At one time I had thought I wanted to go to medical school but the more time I spent in a hospital working in a clinical setting the more I realized I was not cut out for that kind of work. I loved the biology but I was struggling with the procedures - the work was 100% protocol - the same procedures over and over again with zero room for mistakes. So many of the people I worked with were so good at it - they thrived on it.  Me - I had always loved tinkering, taking things apart and trying to put them back together. Trying new things that did not always work was what I liked. Trying this instead of that. What if I did this? What would happen?

But.... when you are dealing with people's lives you can't do that kind of stuff. I have so much respect and envy for people who do this kind of work but I knew it ultimately was not for me. I loved the science but knew I had to change directions with respect to my career. Fortunately, something came along (as it often does in life) that helped me with my dilema.

In the lab one day we started testing a machine called the VITEK for McDonnell Douglas and NASA. VITEK was a fully automated microbial identification and susceptibility system that had been developed in the 1960's for use in space. The system is based on microbial growth in thin plastic identification cards that have small wells with sugars, enzymes, etc. After the cards have been inoculated with sample they are incubated at 37 degrees C and photometrically scanned every hour for either color change or turbidity. Different bacteria ferment different sugars, produce different byproducts, grow or don't grow based on nutrients or conditions, etc. Basically how they grow or do not grow is how they are identified.

McDonnell Douglas was looking to move the product from outer space into the hospital lab and we had engineers coming in and out of the lab weekly tweaking the system. We were running tests in parallel - we'd run a sample using traditional microbiological ID methods and run the same sample through the VITEK, comparing identification results. There was about a three week period when the engineers were in lots - the system was not working properly - something was screwed up in the incubation cycle and they were having a hard time figuring it out.

One of the engineers I had got to know came in with a large stack of green-bar  paper with thousands of lines of code one day. I had never seen actual code before - it was so logical and simple and organized. Really cool! I was able to look at it and quickly pick out where the error was - the incubation line was not properly placed in the incubation cycle loop. I showed the engineer what code lines needed to be swapped around and remember him scratching his head and shrugging his shoulders. Still, he made the mod and....... it worked! It was so trivial but it worked!! The engineers were looking too deeply into the code - this was sort of like a TV not working because it was not plugged in type of thing. That simple. I remember the guy telling me I should have been an engineer. I also remember him telling me the first time someone writes a program it never works and you always had to go back and troubleshoot it. I was intrigued - engineering - could it be for a tinkerer like me who likes to learn from my mistakes?

Well - long story short - my sister and two brothers had degrees in electrical engineering. They had been bugging me for a while to check out engineering. They talked me into going to see Dr Jim Masi (the same Jim Masi who was our first Director at www.ictcenter.org) at Western New England University and we were able to work out an agreement where I could pick up the undergrad courses I was missing and then move into an MS Electrical Engineering program. It took a while and most of the time was incredibly hard but I was able to complete the degree.

As an engineer I could now tinker and try new (sometimes off the wall) things and make mistakes and learn from those mistakes. And that microbiology background has never gone to waste - I know it has helped me think and approach problems a little differently than traditionally trained engineers. All good!