Infinite strength magnetic field?

[aurumdeus]

I first asked this question to my physics teacher, but she was unable to answer me. I was wondering if anyone here could help.

 

The strength of a magnetic field (as with anything else which spreads out evenly in 3 dimentions) operates on an inverse square proportion. As you halve the distance to the origin of the magnetic field, you quadruple the strength of the field. But as you can only take a fraction of the total distance, you can never reach the origin and the strength of the field continues to increase. Surely this would result in a magnetic field of infinite strength, the closer you go? Or if it does not then why is this so?

[BEAKER]

I would think it has to do with the total maximum strength of the original magnet(s) which you could not go beyond.

[infamous]

I first asked this question to my physics teacher, but she was unable to answer me. I was wondering if anyone here could help.

 

The strength of a magnetic field (as with anything else which spreads out evenly in 3 dimentions) operates on an inverse square proportion. As you halve the distance to the origin of the magnetic field, you quadruple the strength of the field. But as you can only take a fraction of the total distance, you can never reach the origin and the strength of the field continues to increase. Surely this would result in a magnetic field of infinite strength, the closer you go? Or if it does not then why is this so?

 

Ask yourself this question aurumdeus: If the initial strength of the magnet were infinite, what is a fraction of infinity? I believe you will agree that one half of infinity is still infinity. Therefore, the initial strength of any magnet cannot be infinite.

[Turtle]

___Wouldn't the smallest possible magnet be a single atom, or if not a single atom then say a molecule of the mineral magnetite? Just search this site for "infinity" & you'll find no end of discussion. In this case, I'd say it's a red herring. ;)

[Kirk Gregory Czuhai]

the magnetic field is caused by the spin states being aligned by the outer electrons in a permanent magnetic or uniform direction flow of a electo-magnetic. another magnetic material can only approach the first so close and no further because of the Pauli-exclusion principle as electrons are Fermions and have anti-symetric wave functions.

[Turtle]

___I believe ;) How many atoms, that is what is the fewest atoms, required to make a permanent magnet? Whichever kind of atoms, ie. element is best I realize may affect the answer. ;)

[BEAKER]

the magnetic field is caused by the spin states being aligned by the outer electrons in a permanent magnetic or uniform direction flow of a electo-magnetic. another magnetic material can only approach the first so close and no further because of the Pauli-exclusion principle as electrons are Fermions and have anti-symetric wave functions.

WOW!;)

[Qfwfq]

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.

 

If the initial strength of the magnet were infinite, what is a fraction of infinity? I believe you will agree that one half of infinity is still infinity. Therefore, the initial strength of any magnet cannot be infinite.

;)

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.

[aurumdeus]

If the initial strength of the magnet were infinite, what is a fraction of infinity? I believe you will agree that one half of infinity is still infinity. Therefore, the initial strength of any magnet cannot be infinite.

I agree that it does not seem right that the magnetic field can have an infinite strength, but the more I think about it the more it seems that it does.

However, in life, this seems obsurd. for example, a bar magnet is comprised of many magnetic particles. even if not infinite, then the strength at the distance from atom to atom must still be phenomenal. Why is it that the magnet does not simply burst apart? even with the strength of the bonds between the atoms, can they really be stronger than the magnetic field at this scale?

[bumab]

You never actually touch the magnets together, and since the ends operate under the inverse square law (i believe), it can still be really strong. the electrons will not touch each other, because of electromagnetic repulsion, and as they get closer, that repulsive force gets stronger.

 

only in collapsed stars can a force overcome the electon repulsion barrier, which is how neutron stars form (the electrons are finnally smashed together with the protons). There is a second barrier, which keeps neutrons from smashing together. If that's also broken by gravity, you get a black hole.

 

Am I correct in that summary? I can't recall the exact terms for it, but it seems to make sense.

[aurumdeus]

Also, this argument can be applied to any 3D field. i only used a magnetic field as an example. for another example, the strength of a gravitational field is also governed by this law. however, as this can be measured to within an object, this can be applied even if fundermental particles do have a volume or size (such as in superstring theory). once again, the closer you go the stronger the attraction, which would once again reach infinity. however, for gravity, this would cause catastrophe, if every mass had an infinite gravitational attraction. it would result in EVERY SINGLE MASS turing into a black hole of infinite strength, which we can be assured they do not. this argument defies more than just common sense, for if a particle experienced a gravitational attraction of infinite strength, it would have infinite potential energy to convert to kinetic enery, which would enable it to reach the speed of light, and maybe even break it, which einstein has told us can not happen. also, if a particle had infinite energy it would have infinite mass (thanks to E=mc^2), which would result in a universe of infinite mas, which brings us to ask the question that if this is so then why is the universe expanding? surely if the universe did have infinite mass then it would simply shrink down to a size of 1/inf? and why did the big bang even occur(if it is the true beginning)?

[aurumdeus]

There is a second barrier, which keeps neutrons from smashing together. If that's also broken by gravity, you get a black hole.

 

I think the barrier that stops the neutrons smashing together is called a coloumb barrier, but i am not sure i am, after all, merely studying at GSCE level and reading a little extra

[bumab]

.however, for gravity, this would cause catastrophe, if every mass had an infinite gravitational attraction. it would result in EVERY SINGLE MASS turing into a black hole of infinite strength, which we can be assured they do not.

 

Not true. The fact that gravity is significantly weaker then the electromagnetic force means that the electro force can hold those partcles apart (through repulsion) and gravity will not be able to overcome it unless you increase the masses involved (solar masses).

[aurumdeus]

Not true. The fact that gravity is significantly weaker then the electromagnetic force means that the electro force can hold those partcles apart (through repulsion) and gravity will not be able to overcome it unless you increase the masses involved (solar masses).

 

but even if the individual particles repel each other a particle will not repel itself from collapsing, which it would if the gravitational field was infinite, which would still produce a point with an infinite gravitational field, regardless of the origin of the point, be it a single particle or an entire star. and once this has been established (which sould take zero time - another problem) if they forces involved are infinite, then the strength of one force compared to the other is irrelevant? even if there was a VERY strong magnetic repultion the infinite gravity would overcome this? but then again this argument can be applied to both forces, so both would be infinite - and if both infinite then how could one triumph over the other?

[bumab]

Oh, I see what you mean. If a particle creates an infinite gravitational field at distance=0, even if it drops off according to the inverse square law, it's still infinite... Well, obviously that's somehow incorrect, but I'm not sure how. Good question. Obviously, gravity can't be infinite at distance=0, or anything for that matter.

 

I seem to recal there was some sort of tunneling effect when distances get super-small, which overcomes the infinite forces that would theoretically occur. I'll try and remember...

[aurumdeus]

I seem to recal there was some sort of tunneling effect when distances get super-small, which overcomes the infinite forces that would theoretically occur. I'll try and remember...

 

i think you are talking about Quantum tunneling, when the wavefunction of a particle 'leaks' across a gap that the particle cannot cross, and if given long enough the particle can be found across the gap. in a more general way, it is as if the particle 'borrows' energy from the surroundings briefly before paying it back.

[bumab]

No, it's not that. Has to do with the energy barrier preventing the electrons from mushing together under a strong enough gravitational field.... I apologize for not remembering the correct term right now, it's been a few years since astronomy.