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phyzguy
phyzguy is offline
#2
Nov25-12, 06:37 AM
P: 2,080
Quote Quote by Blastrix91 View Post
The divergence of a vector field tells us how many field lines goes into a volume element in relation to how many goes out.
So if div B = 0 there should be the same amount of magnetic field lines going into a volume element as are going out of it right?
Correct. Another way to think of it is that magnetic field lines only form closed loops - they can never begin or end.

Quote Quote by Blastrix91 View Post
But the Biot-Savart equations tells us that the magnetic field decreases by r^2 the further away you go. Could somebody help me out in pointing where I got the concept wrong?
The fact that the B field lines never begin or end is not mutually exclusive with a change in the magnetic field intensity. In regions of higher magnetic field intensity, the field lines are "packed closer together", and in regions of low intensity the lines are further apart. Look at the attached image of the B-field of a current loop. The B-field lines are closed loops that are closer together near the current loop and further apart far from the current loop.
Attached Thumbnails
250px-VFPt_dipole_magnetic2.svg.png