Understanding Faraday's Law and the Significance of divB = 0

[r4nd0m]

I'm reading a book on electromagnetism and I am a bit confused about some things in Maxwells equations. This is what I don't like about many physics books: they are very wordy, but at the end you don't know what is an experimental fact, what is a "theorem", what is an assumption and so on,...

Anyway the questions are:

1. Is Faraday's law a consequence of Coulomb's and Biot-Savart's (or Ampere's) law?

2. Is divB = 0 consequence of Biot-Savart's law i.e. if we found the magnetic monopole, would that mean that Biot-Savart's law is not true? (I think so, but I am not 100% sure)

 

[Meir Achuz]

1. No, it is a new law, not envisioned by Coulomb, Biot, Savart, nor even Farady until he discovered it.
2. divB=0 is derivable from the B-S law. and was originally found that way,
but one can start the study of magnetostatics with divB=0 and curlB~j and derive B-S. The two laws are compatible, each derivable from the other.
If a magpole exists, then divB is no longer zero and a Coulomb-like term would have to be added to B-S, but B-S would still give the B field of a current. What EM book are you reading?