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So far Jean-Jacq du Plessis has created 2 blog entries.

## Maxwell’s Equations

Essentially, the entire theory of electromagnetism can be found in the following four equations:

\begin{aligned}\mathbf{\nabla \cdot E} &= \frac{\rho}{\epsilon_{0}} \\ \mathbf{\nabla \times E} &= - \frac{\partial{\mathbf{B}}}{\partial{t}}\\ \mathbf{\nabla \cdot B} &= 0\phantom{\frac{1}{2}}\\ \mathbf{\nabla \times B} &= \mu_{0} \mathbf{j}+\mu_{0} \epsilon_{0} \frac{\partial{\mathbf{E}}}{\partial{t}} \end{aligned}

These are Maxwell’s Equations in differential form, not in integral form, which is the way they are often introduced. I will discuss them in this form, however, as I believe the differential equations convey more elegantly their physical meaning straight from the mathematics. Let’s get started.

### Fields

If you ever did high school physics, you should have some idea of what electric and magnetic fields are. Below is an example of each (depicted using field lines):

What these field lines show is the direction of the respective fields at each location (indicated by arrows) as well as their relative strengths (indicated by density of field lines). So what are these fields actually representing? Well, for electric fields, this shows you the direction an object with a positive electric charge would be forced, while a negatively charged object would feel a force in the opposite direction.…

Let’s do an example. Approximate to 2 decimal places: $\sqrt{40}$
$\sqrt{40} \approx \sqrt{36} +\frac{4}{12} = 6+ \frac{1}{3} \approx 6.33$