I am a physics undergraduate student currently studying electromagnetics. I have previously studied electrostatics and magnetostatics yet the concept of scalar potential, $V$ and the vector potential, A have eluded me.
I understand Maxwell's equations and relevant formulas to calculate them in certain situations and how to go between these quantities and the E and B fields. But I do not understand them conceptually.
I would like to understand their meaning and purpose. If somebody has a good analogy to view these quantities and how they relate to the E and B fields this would be even better.
Please could somebody answer this question and if possible please avoid using too math heavy (some math is expected) approach, so that I can clearly read and understand the concepts presented.
Best Answer
The vector potential has a divergence of zero; we can obtain some intuition by considering the geometry required by the divergence theorem: the volume integral of the divergence of the vector potential is zero for any volume, hence the total net flux through any surface is zero.
So given your specific conditions, you can imagine geometric boundaries and apply this flux rule. This, along with the other conditions, provides some insight into the situation.
The next step is to consider how the curl of the vector potential becomes the magnetic field.