Naked Science Forum
Non Life Sciences => Physics, Astronomy & Cosmology => Topic started by: MathiasArendrup on 27/02/2014 09:36:51
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As far as i can understand, maxwells second equation states that the divergence of the magnetic field is equal to zero. It may be just me misunderstanding the law, but magnets do create a magnetic field around them which attracts opposite dipoles of other magnets right? So how can it be equal to zero?
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Thanks in advance
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Dipole is the key word here. A non-zero divergence tells you that sources exist that send field lines radially outwards (to infinity), whereas dipoles have looping field lines that go out, curve around, and come back to join themselves.
And as you point out, dipoles can certainly interact and attract each other, but that has to do with the nature of dipoles and the force law rather than Maxwell's equation.
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Aha, so you can sort of say, that the dipoles equal eachother out and therefore the divergence is zero?
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Kind of--but an electric dipole exists and the divergence of E is non-zero. What it's really telling you is that the simplest source of a magnetic field is a dipole, whereas the divergence of E being non-zero tells you that the simplest source of the E-field is a monopole. Or put another way, if you try to cut a magnet in half to separate the dipole into two monopoles, you'll end up with two smaller dipoles. Whereas you can chop an electric dipole in half to get two monopoles.
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Thanks! I think i got it pretty well now, i think i didnt quite understand the principle of divergence before, but i do now. Nice explanation thanks
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Another way to say the same that JP wrote: take a closed surface in a magnetic field (for example a sphere): wherever you put that surface, whatever its dimensions, the magnetic field lines entering it are exactly the same (in number) which exit.
You can't *always* do it with electric field: take a closed surface around a single positive electric charge: there will be only field lines exiting the surface, no line entering. The opposite with a negative charge: only lines entering, not exiting.
Divergence is the flux of the field per unit volume inside the surface, in the limit for the volume going to zero. Flux = integral of the field scalar dS, the element of the surface. This is the matematical description of what I have written in words.