Infinite strength magnetic field?

[UncleAl]

Magnetic fields must be at least dipolar. No magnetic monopoles are allowed given Maxwell's equations. You get electric or magnetic monopoles, but not both. Simple dipole field strength varies as 1/r^3.

 

If you derived instead of memorized you would know the trivial answer. Consider a small spherical monopole field source (e.g., a proton). Far field strength varies as 1/r^2 assuming the source is a geometric point. Near field, with your nose up against it, it isn't a point at all. Field strength above an infinite plane does not vary with separation. Bottom line: you asymptote to a maximum value with decreasing radius as the math transitions.

 

Large electric fields cause sparking of the quantum vacuum. An atomic nucleus with Z=1/(Fine Structure Constant) would spark the vacuum into electron-positron pairs and spontaneously inverse beta decay to lower field values.

 

Large magnetic fields are more interesting. The strongest magnets in the universe are magnetars (hypermagnetized neutron stars) with extrenal fields of 10^15 gauss (compared to 10^12 gauss pulsars). Above 4x10^13 gauss the lowest energy electron cyclotron orbit about a field line is still relativistic, m^2c^3/(h-bar)(e). The vacuum itself is now strongly birefringent, and x-ray photons can split and merge without interacting with matter.

[infamous]

The smallest magnet is a lepton, for example an electron. A magnet, however, is a dipole and not a monopole, so the field doesn't go by the inverse square law as it would for a monopole.

 

Let's consider the question for the electric field:

 

If the charge is point-like, as it is for the electron as far as wee can currently detect, then the limit for r --> 0 is indeed infinity. From the classical pov at least.

 

;)

Not a conclusive argument at all, I'd fail you if you wrote that on a calculus test!

 

Of course inf/a = inf, but from that it doesn't follow that the limit can't be inf.

It seems that you and I have a difference of opinion about the definition for infinity. One can do strange things with math if they want to push the envelope, can't they??

[aurumdeus]

Magnetic fields must be at least dipolar. No magnetic monopoles are allowed given Maxwell's equations. You get electric or magnetic monopoles, but not both. Simple dipole field strength varies as 1/r^3.

 

If you derived instead of memorized you would know the trivial answer. Consider a small spherical monopole field source (e.g., a proton). Far field strength varies as 1/r^2 assuming the source is a geometric point. Near field, with your nose up against it, it isn't a point at all. Field strength above an infinite plane does not vary with separation. Bottom line: you asymptote to a maximum value with decreasing radius as the math transitions.

 

Large electric fields cause sparking of the quantum vacuum. An atomic nucleus with Z=1/(Fine Structure Constant) would spark the vacuum into electron-positron pairs and spontaneously inverse beta decay to lower field values.

 

Large magnetic fields are more interesting. The strongest magnets in the universe are magnetars (hypermagnetized neutron stars) with extrenal fields of 10^15 gauss (compared to 10^12 gauss pulsars). Above 4x10^13 gauss the lowest energy electron cyclotron orbit about a field line is still relativistic, m^2c^3/(h-bar)(e). The vacuum itself is now strongly birefringent, and x-ray photons can split and merge without interacting with matter.

 

I will have to take your word for that, as i do not understand the latter half (being at GCSE). however, what happens in the case with gravity? why is it that it is not infinite?

[Qfwfq]

Wheter gravity or electric force, if it goes by inverse square law, a point concentration of charge implies an infinite limit for r --> 0. Of course, it implies an infinite density of charge as well. 20th century physics gives reason to doubt the density could actually be infinite although no spatial size has yet been detected for leptons. From a purely classical pov, however, there is no problem at all.

It seems that you and I have a difference of opinion about the definition for infinity.

I was adopting the definition used in calculus. I don't know which yours is.

[aurumdeus]

doesnt this argument then instantly disprove point particle physics?

[Qfwfq]

not quite

[aurumdeus]

But least provides strong evidence against it?

[Qfwfq]

There are things in particle physics which are even odder.

 

No scattering experiment has yet detected a spatial distrubution for a lepton.

[infamous]

Wheter gravity or electric force, if it goes by inverse square law, a point concentration of charge implies an infinite limit for r --> 0. Of course, it implies an infinite density of charge as well. 20th century physics gives reason to doubt the density could actually be infinite although no spatial size has yet been detected for leptons. From a purely classical pov, however, there is no problem at all.

I was adopting the definition used in calculus. I don't know which yours is.

I'll grant you that Qfwfq; I believe however that the mental concept of infinity goes beyond the bounds of mathematics. You certainly have a right to disagree with this view and I'm rather certain that you will. There are, at least from my point of view, to many paradoxical mathematical answers to the question of infinity. For what it's worth, I'm not convinced that mathematics is up to the challenge, infinity is in fact quite a large problem.

[Qfwfq]

Infinity is a mathematical notion.

infinity is in fact quite a large problem.

Infinity is in fact a veeerrrry, veeeeeeeeeerrrrrrrrrryyyyyyy, vvvvveeeeeeeeeeeeeeeeeerrrrrrrrrrrrrrrrrrrrryyyyyyyyyyyyyyyyyyy large thing indeed. :shrug:

[infamous]

Infinity is a mathematical notion.

Infinity is in fact a veeerrrry, veeeeeeeeeerrrrrrrrrryyyyyyy, vvvvveeeeeeeeeeeeeeeeeerrrrrrrrrrrrrrrrrrrrryyyyyyyyyyyyyyyyyyy large thing indeed. :shrug:

Absolutely Qfwfq; unimaginableeeeeeeeeeeeeeeeeeeeeeeeeee,without understandinggggggggggggggggggggggg,undescribablelyyyyyyyyyyyyyyyyyyyyyyy,by any methoddddddddddddddddddddd,known to mannnnnnnnnnnnnnnnnnnnnnnnnnnnnnnn..............................................

[bumab]

Uhhh.... back to the topic, and the aforementioned link I promised:

 

http://www.daviddarling.info/encyclopedia/E/electron_degenerate_matter.html

 

It's not much, but it defines the electron degeneracy limit, which is what I was trying to allude to earlier, although I forgot the name at the time. Using that value, I assume you could determine the upper limit of the an electromagentic force (strong or weak, don't remember which), since that limit must be broken for the collapse of a white dwarf into a neutron star. Either way, it shows an upper limit to a force which appears to have an infinite value at d = 0

[Qfwfq]

Using that value, I assume you could determine the upper limit of the an electromagentic force (strong or weak, don't remember which), since that limit must be broken for the collapse of a white dwarf into a neutron star.

Hmmm, wouldn't that have more to do with weak interaction? I mean, akin to the reverse process of beta decay. Applying Fermi's rule one could work out the cross section, it ought to be quite low, making it hard to crush things into neutrons...

[maddog]

To speculate upon an infinite potential E or B field for as d=0 is a bit silly. To calculate the B field of an

object at a point in space is only dependent upon the charge density below this point. So as d -> 0,

the potential doesn't go to infinity (though I do agree with Qfwfq - that some fancy Calculus is

needed to show a value like a/b -> 0/0 is found to be not true: L'Hospital's Rule, etc). Yes, we would

be talking about dipole (or higher) field types (not monopole).

 

maddog

[textron45]

Possibly one must consider the Planck distance implication when trying to resolve this problem. At the Planck scale, the distance dimension breaks down, or rather reaches a limit to where distance can no longer be classically reduced or "cut in half". One would then have to travel "around" that last infinitesimily small Planck distance unit, something which we do every day when we or anything else in our macro world engages in motion. Otherwise, we could never move at all. This movement, then, would of necessity require travelling through a much smaller 5th,6th,7th., etc., dimension, something which at present is theoretical, but which is nevertheless considered viable in string theory and other multi-dimensional theories. In short, you WILL eventually reach the source of the magnetic field, and then the limit to its power will also be reached.