I could not get, withinh the time I spent a nice short description or a video explaining the scalar and vector potentials from scratch.

Here I reproduce two examples I stumbled upon, while searching for suitable page/video for a quick reminder of scalr and vector potentials. These videos on You Tube show hazards of learning from internet. I have reproduced only the relevant parts of the videos.

FIRST VIDEO : Watch from time 1:30 to 3:05 sec

The speaker cancels div in equation

\[\text {div} B = \text{div . curl }A\]

and gets \(B=\text{curl} A\)

SECOND VIDEO: Watch from time 0:50 to 2:00 Mins

The speaker compares \[ div B = 0 \qquad \text{and} \qquad div curl A=0 ]\ and concludes the equality

\(B=curl A\)

If you accept the logic given in these two videos, you can prove anything equals anything.

So, for example, it is definitely correct that \(\text{div 5} =\text{div} 37\), because both sides are zero.

It should then follow that \(5=37\),

I wish life was a simple as made out in the two videos.

The correctness of the final answer does not justify the means of getting the result.