13. Introduction

The four fundmental forces of nature are known to be:

• Nuclear Strong

• Nuclear Weak

• Electromagnetic

• Gravity

The main difference between the top two and bottom two are their range, nuclear forces are short range and really exist only within the confines of an atmomic nucleus. The bottom two forces are long range forces, which in their classical form follow inverse square laws (Coulomb’s and Newton’s respectively).

As we will see, electrostatics and the study of electric fields is often treated as one separate theory and the theory of magnetism can be thought of quite separately, however as we will see from a picture of moving charges and then Faraday’s law, bringing the two theories together into electromagnetism is a major achievement.
James Clark Maxwell’s big contribution to classic physics is electromagnetism - in order to see this clearly, he wrote his much celebrated equations in differential form, see Equation (22.5). A lot of modern physics, such as quantum field dtheory and the standard model of particle physics relies on this unified formulation of electromagnetism.

In this section we will cover the mathematical basics of electric fields, using flux. This will leads us into Gauss’s law which is a key idea in electrostatics and can be applied to many other analogue physical systems. We can then find an analoguous system of fields ionvolved in Magnetism, which through Ampère’s law allows us to link currents with magnetism. Faraday’s law finally allows us to go back from magnetic fields to produce potential differences and therefore electric fields. We finish with a discussion of Maxwell’s equations in differential form, in contrast to the integral form of equations that we started with.