# How does magnetism work?

1. Oct 26, 2005

### daniel_i_l

GR explains how gravity works. Is there a similar explanation for magnetism. Maxwell showed that magnetism and electricity are two sides of the same coin. And I understand that electricity is a flow of electrons. Can that help me understand magnetism?

2. Oct 26, 2005

### Mk

I think you are looking for how electricity and magnetism are "two sides of the same coin." Or maybe it is what's going on that causes magnetism?
I think its the second one.

I'll outline it for you:

There are different types of magnetism, lucky for you, the three main being: Diamagnetism, Paramagnets, and Ferromagnetism. We'll go backwards.

Ferromagnetism is the kind you normally observe. Refrigerator magnets, speaker magnets, wallet magnets, permanent magnets.

Ferromagnetism is due to the direct influence of two quantum effects: quantum spin, and the Pauli exclusion principle.
The spin of an electron, (something you can't visualize correctly) combined with its orbital angular momentum, results in a magnetic dipole moment and creates a magnetic field. (if you need to, you can imagine the electrons spinning around). The dipoles tend to align spontaneously, without any applied field.

Ferromagnetism manifests itself in the fact that a small externally imposed magnetic field, say from a solenoid, can cause the magnetic domains to line up with each other and the material is said to be magnetized. The driving magnetic field will then be increased by a large factor which is usually expressed as a relative permeability for the material. Ferromagnets will stay magnetized after having been aligned to this exterior magnetic field. Called hysteresis. The fraction of the saturation magnetization which is retained when the driving field is removed is called the remanence of the material.

All ferromagnets have a maximum temperature where the ferromagnetic property disappears as a result of thermal agitation -- the Curie temperature. You know that heat is actually just the atoms shaking around, after the atoms shake around enough they aren't all aligned the same way!

So really, all the electrons are "spinning" the same way, and that creates the field.
http://hyperphysics.phy-astr.gsu.edu/hbase/solids/imgsol/domain.gif

Diamagnetism is a very weak form of magnetism, that needs another magnetic field to work. It is the result of changes in the orbital motion of electrons. Diamagnetism is repelling. Diamagnetism is found in all materials; however, because it is so weak it can only be observed in materials that do not exhibit other forms of magnetism. Some diamagnetic materials that should be recognized are water, pyrolitic graphite, and superconductors.
http://www.exploratorium.edu/snacks/diamagnetism_www/ [Broken]

Paramagnetism is closely related to diamagnetism, and also needs an external magnetic field. It occurs temporarily, when its magnetic dipoles align with the external field. Some paramagnetic materials that should be known are oxygen, aluminum, and sodium.

Last edited by a moderator: May 2, 2017
3. Oct 26, 2005

### rbj

nearly everything that Mk wrote is correct, but IMO, is not the root issue. (where does the magnetic field come from?)
Maxwell showed that magnetism and electricity are interactive. that they have something to do with each other, but it wasn't until special relativity that they were shown to be "two sides of the same coin". one can use SR to show that the magnetic field is nothing other than the electrostatic effect, but taking into consideration time-dilation from SR. here is something i posted here long ago about it:
The classical electromagnetic effect is perfectly consistent with the lone
electrostatic effect but with special relativity taken into consideration.
The simplest hypothetical experiment would be two identical parallel
infinite lines of charge (with charge per unit length of $\lambda \$ )
and some non-zero mass per unit length of $\rho \$ separated
by some distance $R \$. If the lineal mass density is small enough
that gravitational forces can be neglected in comparison to the electrostatic
forces, the static non-relativistic repulsive (outward) acceleration (at the instance
of time that the lines of charge are separated by distance $R \$)
for each infinite parallel line of charge would be:
$$a = \frac{F}{m} = \frac{ \frac{1}{4 \pi \epsilon_0} \frac{2 \lambda^2}{R} }{\rho}$$
If the lines of charge are moving together past the observer at some
velocity, $v \$, the non-relativistic electrostatic force would appear to be
unchanged and that would be the acceleration an observer traveling along
with the lines of charge would observe.
Now, if special relativity is considered, the in-motion observer's clock
would be ticking at a relative *rate* (ticks per unit time or 1/time) of $\sqrt{1 - v^2/c^2}$
from the point-of-view of the stationary observer because of time dilation. Since
acceleration is proportional to (1/time)2, the at-rest observer would observe
an acceleration scaled by the square of that rate, or by ${1 - v^2/c^2} \$,
compared to what the moving observer sees. Then the observed outward
acceleration of the two infinite lines as viewed by the stationary observer would be:
$$a = \left(1 - v^2 / c^2 \right) \frac{ \frac{1}{4 \pi \epsilon_0} \frac{2 \lambda^2}{R} }{\rho}$$
or
$$a = \frac{F}{m} = \frac{ \frac{1}{4 \pi \epsilon_0} \frac{2 \lambda^2}{R} - \frac{v^2}{c^2} \frac{1}{4 \pi \epsilon_0} \frac{2 \lambda^2}{R} }{\rho} = \frac{ F_e - F_m }{\rho}$$
The first term in the numerator, $F_e \$, is the electrostatic force (per unit length) outward and is
reduced by the second term, $F_m \$, which with a little manipulation, can be shown
to be the classical magnetic force between two lines of charge (or conductors).
The electric current, $i_0 \$, in each conductor is
$$i_0 = v \lambda \$$
and $$\frac{1}{\epsilon_0 c^2}$$ is the magnetic permeability
$$\mu_0 = \frac{1}{\epsilon_0 c^2}$$
because $$c^2 = \frac{1}{ \mu_0 \epsilon_0 }$$
so you get for the 2nd force term:
$$F_m = \frac{v^2}{c^2} \frac{1}{4 \pi \epsilon_0} \frac{2 \lambda^2}{R} = \frac{\mu_0}{4 \pi} \frac{2 i_0^2}{R}$$
which is precisely what the classical E&M textbooks say is the magnetic force (per unit length)
between two parallel conductors, separated by $R \$, with identical current $i_0 \$.

Last edited: Oct 26, 2005
4. Oct 26, 2005

### Manchot

You can also show that the converse of what rbj showed: that you can derive Special Relativity effects from the apparent contradiction of the magnetic force. If you consider two protons moving in the same direction parallel to one another, then in the "stationary" reference frame, there is a magnetic force pulling them together in addition to the electrostatic one pushing them apart. On the other hand, in their own reference frame, there is no magnetic force between them, just an electrostatic one pushing them apart. It turns out that the ratio of the two net forces exactly corresponds with the measured time dilation in the two reference frames.

5. Oct 26, 2005

### daniel_i_l

WOW!! Thanks A LOT!! That is really cool, and I couldn't have hoped for a nicer answer! correct me if I'm wrong - the magnetic force can be thought of as deacceleration (attractive acceleration) caused by relavistic effects!

6. Oct 26, 2005

### rbj

it's pretty close, IMO. you would have to come up with a little different explanation if the two infinite lines were moving in opposite directions. then, in the classical POV, the magnetic force would team up with the electrostatic repulsion.

this didn't really prove to whole enchilada, it was a special case where you could show that in a situation where there was no separate magnetic action existing, that knowing about electrostatic action and effects of relativity upon an observer, that the end result observed is identical to the case where there was no such thing as time-dilation but there was this extra separate magnetic force (the classical POV).

the effect of time-dilation means that the outward acceleration of the two indentical lines of charge appears slower when the lines are moving past an observer, than if they were not moving past that observer. classical E&M says they are slowed down by an opposing magnetic force, relativistics mechanics says they appear to be slower than they would be if you were moving alongside the moving lines (which is identical to if they, and you, were both "stationary").

7. Oct 26, 2005

### daniel_i_l

I just thought of something, if magnetism isn't really a force, just changes in acceleration then according to the equivilance principle shouldn't magnitism be indistinguishable from gravity ... it isn't?
and how does this explain how a bar magnet works? (if the answer to my first question is yes then I'd know the answer to this one)

8. Oct 26, 2005

### rbj

i don't get how you would even draw such a conclusion. electromagnetic charge is not at all the same stuff as graviational charge. one of the axioms that makes GR work is the Equivalence Principle that says that, in all cases, gravitational mass (a.k.a. "gravitational charge") is the same exact stuff that inertial mass is. that's how you can come up with these thought experiements of Einstein in the elevator decending at 9.8 m/s^2 being the same as weighlessness and Einstein in the spaceship accelerating at 9.8 m/s^2 being the same as standing on the earth. you just can't do that with E&M charge. they ain't the same.

9. Oct 27, 2005

### µ³

What happens when you apply the same concept to gravity? Is there a force caused by a mass moving at a certain speed?

10. Oct 27, 2005

### daniel_i_l

I know that magnetism and gravity are totally different as magnetism isn't connected to mass, it just looked like an interesting connection if you say that like gravity, magnetism isn't really a force. Or did I misunderstand? Thanks again to everyone!

11. Oct 27, 2005

### Mk

Electromagnetism is a force.

12. Oct 27, 2005

### daniel_i_l

Do you mean that EM is a force but not magnetism by itself, or are they each a force both seperatly and together, or are they both forces only together cause magnetism has meaning only with electricity as the relevistic view could imply.

13. Oct 27, 2005

### El Hombre Invisible

There are four fundemental forces, one of those is the electromagnetic force. Then there are lots of other 'forces' that aren't fundemental - they are special to the system being described. The 'electric' and 'magnetic' forces are such forces, as are 'contact' force, 'normal reaction', 'friction', etc. All are phenomena caused by the electromagnetic force. So when we say 'the electric force' or 'the magnetic force', we are using the term more loosely than when we refer to the fundemental forces.

It occured to me that QED, as far as I know, is non-relativistic, and yet also explains electric and magnetic forces. Does it offer an entirely different explanation?

EDIT: I mean, of course, an explanation for the magnetic force's relationship to the electric force, just in case someone was going to say: "yes, it's mediated by photons".

Last edited: Oct 27, 2005
14. Oct 27, 2005

### daniel_i_l

What do you mean when you say that they're special to the the system being described? Could you please explain alittle more? Thanks!

15. Oct 27, 2005

### El Hombre Invisible

Just as rbj stated earlier. You can have the same phenomena be observed as electrostatic in one inertial frame, and as magnetic in the other.

If you have two lines of static charge parallel to each other, the electromagnetic force between them would be what we call the electrostatic force. However, if those charges are moving with velocity v compared to the observer, you can describe the force acting between them as magnetic, or a mixture of electric and magnetic. Since both set-ups are equivilent, that is they depend only on the reference frame in which they are observed, we describe them as electric or magnetic forces due to the circumstance under which they are observed. In other words, in one special circumstance we describe the force as electric. In another, we describe it as magnetic.

With the other 'forces' it is a bit different. We understand that the contact force acting on one body by another is electromagnetic in nature. It is overwhelmingly easier, however, to describe the force as a contact force. Likewise friction is exactly the same phenomenon, but under different circumstances again. We don't call the contact force the friction force or vice versa, despite it fundementally being the same force. Hence each of these phenomena are described as a 'force', but all of them are electromagnetic in nature.

16. Oct 27, 2005

### rbj

the answer is yes, sorta. check out:
http://en.wikipedia.org/wiki/Gravitomagnetism#Gravitomagnetism_vs._electromagnetism
and you will see an identical set of Maxwell's Equations except that charge density is replaced by mass density and $$-G \rightarrow \frac{1}{4 \pi \epsilon_0}$$. all that makes sense. you could set up the same thought experiment with two lines of mass (and their attraction toward each other would be ostensibly attenuated, from the POV of the "stationary" observer, by a gravitomagnetic force).
one difference, that i do not understand is this "spin 2" thing that apparently doubles the gravitomagnetic force from what we would expect. someone else will have to explain that. these were derived from the Einstein Field Equation under conditions of slow speed and reasonably flat spacetime.

Last edited: Oct 27, 2005
17. Oct 27, 2005

### daniel_i_l

Thank you for the clear answer!

18. Jun 11, 2009

### bhornbuckle75

I was reading some of the other replies, and I just didnt get this into I read yours. Where you say "two lines of static charge parralel to each other" the other(s) said two 'infinite' lines. Thats what kept hanging me up. I kept trying to visualize the concept of an infinite line in motion, and what exactly that meant. A line that is infinite, in my mind, could not move parallel to another infinite line, since both are infinite - where would they be able to go if they already existed infinitely parallel to each other, it seems they would have to be at rest if they are to remain parallel. I thought that perhaps I was misunderstanding the concept of "parralel" in the nature of this thought experiment, however this was even more confusing. My question then is what was the meaning of "line", was this meant to be a physical line which is staticly charged? as I was taking it. Or - the way I understand it now - was it simply to mean a charge which is moving along an infinite line. Or is there some product of the nature of "charge" which in order for the thought experiment to work, must be thought of as infinite. For instance a charge which is not an infinite line, but for this concept to work right must be thought of as if it is an infinite line.

19. Jun 11, 2009

### PatPwnt

Instead, think of an electrically neutral wire with a current going through it. If you are a charged particle, say an electron, at rest with respect to the wire, you do not feel any force from the wire and it doesn't feel anything from you. There is a current in the wire, which means there's moving charge, but there is an opposite stationary charge to give zero net charge. This also means the moving charge is length contracted in your frame. If the current is a flow of electrons, and you start to move in the direction of these electron, they will become less length contracted and the negative charge density will decrease in your frame. The once stationary positive charges in the wire will now be moving in your frame and become more length contracted and give a higher charge density of positive charge. Since you are a negative electron, you will be attracted to the wire. This is my understanding of magnetism. Seems simple to me.

20. Jun 12, 2009

### bhornbuckle75

Ok I had to think about your explanation for a second to understand it. Ive taken college courses in humanities and havent had much of a formal education in science, and am mostly self taught in that area-so I think I have to digest some of the terms a bit to understand them. I am having a bit of trouble understanding the concept of length contraction. Is this an eisntein thing about things moving faster the more contracted and dense they will be when doing so? (this is how I am taking it anyway). I understand then that as I (being an electron) start to move with the electron current in the wire, they will seem less contracted, however this will be because I too will be more contracted, since I am moving with them correct? What I dont understand is why would the stationary charge be more contracted-would it not be that, since I am more contracted and would have a higher charge density myself-that I myself would be more attracted because of my higher cd? rather than vice versa?
Also, to bring it back home-how does all of this explain - for instance - the electric mechanism at work with a piece of metal being attracted to a magnet.