Introduction

What is electromagnetic theory anyway? Is it the study of magical, invisible and super cool energy? Well, it kinda is! So what‘s it any good for? In this blog we are going to explore this alluring black magic to get an understanding of what it actually is.

Electromagnetism is a branch of physics that deals with the interaction between electrically charged particles and magnetic fields.

Simply put, an electric current flowing through a wire creates a magnetic field around the wire. This magnetic field can be used to create a magnet out of the wire, called an electromagnet.

In turn, a magnetic field can induce an electric current in a nearby wire. This is for example how a modern day generator works - by rotating a wire coil in a magnetic field, it generates an electric current in the wire.

Electromagnetic waves are also used for television broadcasts, cell phones, Bluetooth, radio, and every other form of wireless technology and communication.

Magnetic and electric Fields - Electromagnetic fields

Electromagnetic fields are a combination of invisible electric and magnetic fields of force. They are generated by natural phenomena like the Earth's magnetic field but also by human activities, mainly through the use of electricity. Figure 1 below illustrates such a wave from and through an object. We notice how the wave turns around the object, as we learned it does with wires.

Figure 1: Illustration of a magnetic field through an object.

In daily life magnetic fields are all around us. We are all, to a greater or lesser degree, exposed to electromagnetic fields. Examples are the fields produced by kitchen appliances, radio transmitters and mobile phones. A changing magnetic field can create an electric field, which can be considered to be wireless energy. This takes us to Maxwell's equations. Maxwell's equations are a set of four fundamental equations in electromagnetism that describe the behavior of electric and magnetic fields and their interactions with each other.

Maxwell's equations

Gauss's law for electric fields

This equation relates the electric field to the charge density in a given region of space. It states that the electric flux through any closed surface is proportional to the charge enclosed within the surface - wihtin the closed surface. Ok, excuse me - what? Let’s go through that again step by step.

In simpler terms, imagine a ball with a bunch of electric charges inside it. If you draw an imaginary surface around the ball, then the total amount of electric flux through that surface is proportional to the amount of electric charge inside the surface.

The imaginary surface we drew from the ball indicates the closed surface. A closed surface contains a volume of space, enclosed from all directions; It consists of one connected, hollow piece that has no holes. So for example the object in the illustration shown in Figure 1 is a closed surface. Another way to think of it, is to imagine a rubber band. A rubber band is a closed surface as well. But if you cut the rubber band so it has two ends, it’s no longer a closed surface.  

Now we just need to understand what flux is. Flux is a term used in physics to describe the flow or movement of something through a surface or boundary.
Imagine you have a water hose and you point it at a wall. If you turn on the water, the water will flow out of the hose and hit the wall. The water hitting the wall is an example of flux - the water is flowing (or "fluxing") through the boundary (the wall).

In physics, the term "flux" is often used to describe the flow of all kinds of things and not just water. Flux can therefore be measured in different units depending on the quantity being measured. Right now we are for example interested in the flow, the flux, of electric and magnetic fields.

Okay, so now we understand all the words and principles behind Gauss’s Law for electric fields - this will help us to understand the three other laws much better as well.
The mathematical formula for Gauss's law is a bit more complicated, but it essentially says the same thing: It relates the electric flux through a closed surface to the total charge enclosed by that surface.

Gauss's law for magnetic fields

This equation relates the magnetic field to the magnetic charge density in a given region of space. It states that there are no isolated magnetic charges in nature, and the magnetic flux through any closed surface is always zero.

This means that the sum of all magnetic field lines entering a closed surface is equal to the sum of all magnetic field lines leaving the surface. What comes in goes out.

This might seem counterintuitive, since we often think of magnetic field lines as starting and ending on magnetic poles. However, Gauss's law tells us that for any closed surface, the number of field lines entering the surface must be equal to the number of field lines leaving the surface, regardless of where they start or end.

Faraday's law of electromagnetic induction

This equation describes how a changing magnetic field can create an electric field. It states that the electric field induced in a closed loop is proportional to the rate of change of the magnetic flux through the loop.
This phenomenon is known as electromagnetic induction and it forms the basis for the operation of generators and transformers, as well as many other electrical and electronic devices. 

Ampere's law with Maxwell's correction

This equation relates the magnetic field to the current density in a given region of space. It states that the magnetic field induced around a closed loop is proportional to the current passing through the loop, with a correction term that accounts for the time-varying electric field.

Together, these equations provide a complete description of the behavior of electric and magnetic fields and their interactions with each other. They form the foundation of classical electromagnetic theory. If you want to learn the specific math for these equations, you can visit here to get started.
These equations have been extremely useful in developing technologies that rely on electromagnetic waves, such as radios, televisions, cell phones, and medical imaging devices. Overall, electromagnetic theory is a fundamental part of our understanding of the physical world, and it has had a profound impact on our technology and way of life.