Introduction

What is electromagnetic theory, really? Is it the study of magical, invisible, super-cool energy? In a way, yes! So what is it useful for? In this article, we will explore this intriguing magic to understand what it actually is.

Electromagnetism is a branch of physics dealing 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 turn the wire into a magnet, called an electromagnet.
A change in magnetic flux through a wire loop can induce a voltage and, in a closed circuit, a current. This is how a modern generator works, for example: rotating a coil in a magnetic field generates current in a wire. Electromagnetic waves are also used for television broadcasting, mobile phones, Bluetooth, radio, and every other form of wireless technology and communication.

 

Magnetic and Electric Fields - Electromagnetic Fields

Electromagnetic fields combine invisible electric and magnetic force fields. They arise from natural phenomena such as Earth’s magnetic field, and from human activities, mainly the use of electricity. Figure 1 below illustrates magnetic field lines around and through an object. Field lines show the field direction; they are not themselves electromagnetic waves.

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

Magnetic fields surround us in everyday life. We are all exposed to electromagnetic fields to some degree. Examples include the fields produced by kitchen appliances, radios, and mobile phones. A changing magnetic field can generate an electric field, which can be viewed as wireless energy. This brings us to Maxwell’s equations: four fundamental equations of electromagnetism describing the behaviour of electric and magnetic fields and their interactions.

 

Maxwell’s Equations

The four fundamental equations of classical electromagnetism were formulated by James Clerk Maxwell in the 19th century and are still used in many areas of physics today. The four Maxwell equations are Gauss’s law for electric fields, Gauss’s law for magnetic fields, Faraday’s law of electromagnetic induction and Ampère’s law with Maxwell’s correction.

 

Gauss’s Law for Electric Fields

This equation relates the electric field to the charge density in a region of space. It states that the electric flux through any closed surface is proportional to the charge enclosed by that surface. Sorry, what was that? Let us go through it step by step.

Imagine a ball containing many electric charges. Draw an imaginary surface around it: the total electric flux through this surface is proportional to the amount of electric charge inside it.

The imaginary surface drawn around the ball is the closed surface. A closed surface encloses a volume from all directions. It consists of a connected hollow surface without openings. For example, the object illustrated in figure 1 is a closed surface. Think of the intact surface of a balloon enclosing a volume. A rubber band instead forms a closed curve, not a closed surface in three dimensions.

Now we just need to understand what flux means. In physics, flux describes the flow or movement of something through a surface or boundary.

Imagine pointing a hose at a wall and turning on the water. The water flows out and hits the wall. The water flow through an imaginary surface just in front of the wall illustrates flux. Water does not need to pass through the wall itself.

In physics, the term flux is often used for the flow of many things, not just water. Flux can therefore have many different units. Here, for example, we are interested in the flux of electric and magnetic fields.

Now we understand the terms in Gauss’s law for electric fields better, which will help us understand the other three laws.

The mathematical formula for Gauss’s law is a little complicated, but describes the same relationship: electric flux through a closed surface is related to the total charge enclosed by it. To learn more about the mathematics and try calculations yourself, a link further down leads to a website with all the formulas discussed in this article.

 

Gauss’s Law for Magnetic Fields

In classical electromagnetism, this equation states that the magnetic field has zero divergence: no isolated magnetic monopoles are included. The net magnetic flux through any closed surface is zero.

This means that the sum of magnetic field lines entering a closed surface equals the sum leaving it. What goes in comes out again.

This may seem counterintuitive because we often picture magnetic field lines starting and ending at magnetic poles. But Gauss’s law says that for any closed surface, the number of field lines (flux) entering equals the number leaving. Magnetic field lines do not start or end at the poles; they continue through the magnet.

 

Faraday’s law of electromagnetic induction

This equation describes how a changing magnetic field can create an electric field. It states that the induced electromotive force around a closed loop equals minus the rate of change of magnetic flux through it. This phenomenon is electromagnetic induction, which, as mentioned, underlies generators, transformers, and many other electrical and electronic devices.

 

Ampère’s law with Maxwell’s correction

This equation relates the magnetic field to current density in a region of space. It relates the circulation of the magnetic field around a closed curve to the current through a surface bounded by the curve, plus a displacement-current term arising from the time-varying electric field.

Together, these equations provide a complete description of electric and magnetic fields and their interactions. They underpin classical electromagnetic theory. To learn more about the specific mathematics, look here to get started.

These equations have been extremely useful in developing technologies such as radios, televisions, mobile phones, and medical imaging equipment. Electromagnetic theory is a fundamental part of our understanding of the physical world and has profoundly influenced our technology and way of life.