Thread: Div B = 0? I don't get it View Single Post

 Quote by Blastrix91 When you say div B = 0 mean that magnetic field lines only forms closed loops, is that in the moment a magnetic field begins and end (if that were to happen) there would be a change in what goes in in relation to what goes out and thus div B wouldn't be 0? That at least makes sense to me. The B described in Biot Savarts law is the same that is described in div B = 0 right? So from a pure mathematical standpoint div B shouldn't be 0 if it is decreased by r^2 the further in the coordinate system you go. If you get what I'm saying?
I get what you are saying, but your intuition is wrong. Take the case of a simple dipole field, where:
$$\vec B = K(\frac{3\vec r (\vec m \cdot \vec r)}{r^5}-\frac{\vec m}{r^3})$$

where K is a constant, m is a constant vector in the direction of the dipole, and r is the radius vector. It satisfies divB = 0, but falls off as 1/r^3 at large r. Try it! If you plot it out, what you will see is closed loops which are closer together near the center and further apart as you move away from the center, as I said earlier.