Maxwell's Equations: Gauss' Law Explained (ft.  

Can YOU understand Gauss Law, which is the Maxwell Equation that prescribes how Electric Fields must behave?
Hey everyone, I'm back with another video! This one was highly requested, as a follow-up to my first two Maxwell Equation videos. This, therefore, is the third video in the series discussing these equations of Electromagnetism. The particular equation discussed here is also known as Gauss' Law.
It essentially tells us that the divergence of an electric field must be equal to the charge density within the volume of divergence, divided by epsilon nought (permittivity of free space). We will discuss exactly what all of these words mean. We will talk about vector fields, of which an electric field is an example, and how we can take the divergence of a vector field. We will visualise how electric fields behave, and with the help of Higgsino Physics, we will see just how the divergence operator behaves on vector fields. Finally, we will see how to calculate the charge density in a particular region of space, and link the two sides of the Gauss' Law equation together.
Massive thanks to Higgsino Physics for contributing such a brilliant explanation of what divergence means! I highly recommend you head over to his channel and subscribe if you haven't already - you can find him here: ‪@Higgsinophysics‬
Maxwell's Equations of Electromagnetism are a full classical description of the behaviour of electric and magnetic fields, as well as any emergent electromagnetic phenomena (such as EM waves - light). I will also briefly compare the Gauss' Law equation discussed in this video, to the equation I discussed in the first video in this series - Gauss' Law for Magnetism. While that equation told us that the divergence of any magnetic field must always be zero, resulting in the non-existence of magnetic monopoles, the equation for electric fields is slightly different. It tells us that the divergence of an electric field can be nonzero, thus allowing the existence of electric monopoles. These electric monopoles are more commonly known as charges (or charged particles)! You can watch all the Maxwell Equation videos I have made in this playlist here: • Maxwell's Equations EX...
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Thanks for watching and I'll see you really soon!