Note on the magnetic vector potential

This post is from an earlier year, meaning the information here is likely outdated. You should look for a newer post from the current year to get the newest exercises and notes.

Magnetic dipole (Source: Wikipedia*)

In electrostatics we found it very convenient to introduce the concept of the electric potential. It gave us a straight forward way of calculating electric fields without doing any vector calculations or using any symmetry arguments. Can we introduce something similar for magnetic fields?  It turns out that because magnetic fields are divergence less we can find a vector potential who’s curl gives us the magnetic field! Even though this magnetic vector potential is not as useful as the electrostatic potential in elementary applications, it turns out to be of major importance in electrodynamics as well as classical mechanics and quantum mechanics. It might therefore be a good idea to get familiar with the concept and some of it’s properties already, especially if you are taking a degree in physics. In this note I explain how to find the vector potential, the concept of a gauge transformation and it’s fundamental equations relating it to currents in both electrostatics and electrodynamics. Read more here:

* Image found at / CC BY-SA 3.0

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