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.