The force between two adjacent magnets
Michael W. Hicks
typical magnet works -- more specifically, how do two magnets attract or
repel one another? I do understand a few of the fundamentals of magnetism.
For example, I'm aware of the fact that moving charges create a magnetic
field. I'm familiar with the "right-hand rule" whereby one grasps a current
carrying wire in his or her right hand with the thumb pointing in the
direction of the current, and then the fingers circling around the wire will
be in the same direction as the resulting magnetic field. I understand how a
current passing through a magnetic field experiences a force that's
proportional to the component of the magnetic field that is perpendicular to
the wire and the force is directed in such a way so as to be at a right
angle to both the direction of the current and the magnetic field. From
this, I can clearly see how two parallel current streams experience a force
that pulls them together, while two anti-parallel current streams experience
a force that pushes them apart. Furthermore, I understand how a coil or
solenoid combines the field of the coils in such a way to make a uniform
magnetic field within its interior.
However, from all this, I'm having trouble understanding exactly how two
simple magnets would attract or repel one another. I suppose my
understanding of the magnets themselves is rather poor. As I understand it,
magnets are made up of a number of domains, each of which is basically a
little magnet... I assume (perhaps wrongly) that these domains are like
little coils, and all of them are roughly aligned in the same manner. But
still, it seems to me that the force that these (spinning?) domains would
experience would not tend to cause the magnets to attract or repel each
other. Can someone clarify this for me please? TIA!
Igor
Most permanent magnets, especially bar magnets, are magnetic dipoles.
So are closed circular loops of wire with current flowing through
them. That should be enough to point you in the correct direction.
Joseph.D.Warner
Michael W. Hicks wrote:
> However, from all this, I'm having trouble understanding exactly how two
> simple magnets would attract or repel one another. I suppose my
> understanding of the magnets themselves is rather poor. As I understand it,
> magnets are made up of a number of domains, each of which is basically a
> little magnet... I assume (perhaps wrongly) that these domains are like
> little coils, and all of them are roughly aligned in the same manner. But
> still, it seems to me that the force that these (spinning?) domains would
> experience would not tend to cause the magnets to attract or repel each
> other. Can someone clarify this for me please? TIA!
No permanent magnets are made from material that has an imbalance in the
direction that the electron dipoles points. (OK this does apply to
nuclear dipole moments too but you only see that affect at very low
temperatures.) Basically all 1/2 spin particles like electrons, protons
and neutrons have an intrinsic magnetic dipole. (Not getting into the
difference between metal ferromagnets and ceramic ferromagnets, I'll
proceed.) At temperatures below the Curie point the magnetic dipoles of
the outer most electrons in the atoms spontaneously and cooperatively
align themselves. The force that aligns them is called the Exchange
Force. It comes from the many particle interactions between the atoms.
The general theory takes the complete interaction Hamiltonian and then
applies a simplifying model to it that reflects the symmetry of the
atoms. From that Hamiltonian you can get the energy levels of the
electrons for different spin states. Then apply the Fermi-Dirac
distribution you can get the number of electrons in each spin state
versus temperature. From that you apply the thermodynamic equations and
calculate the magnetic susceptibility and you can see that at some
temperature the magnetic susceptibility goes to infinity. That
temperature is called the Curie point.
Now how close that point is to the measured point depends on the
accuracy of your model. But it is useful to see why there are permanent
magnets. After you have done that you can apply other theories to
minimize the energy of the system below the Curie point and you will see
the structure break up in magnetic domains some crystal directions. But
with each domain all of the magnetic moments of the electrons points in
the same direction.
What you can do now with the domains you can model teh problem with all
the magnetic dipoles pointing in the same direction with each of your
two magnetics (or if you want you can have some of the domains pointing
in anyother direction). Using the standard force equation of the force
between magnetic dipoles F =A/r^3 where A is a constant of the material
and r is the distance between the dipoles. Also, you need to times that
by an unit directional vector to reflect the position and orientation of
the atom and each of the dipoles. That you can get out of Jackson or
anyother EM text book. After you have calculated the force between each
atom do to everyother atom you then just need to sum up all the forces.
Depending how detail you like to do and how much you like to approximate
the problem, the calcuation of the force between two magnets can take
between a few minutes to a year or more of computer time.
Michael W. Hicks
news:d434b6c6.04072...@posting.google.com...
I'm still confused. To my knowledge, if you placed one magnetic coil near
another, they would tend to align themselves in the same direction. From
that, I don't see how they would either be pulled together or repelled
apart. I'm just not seeing it from the diagrams I construct.
Again, the alignment aspect I understand. But the attraction/repulsion part
is still confusing me.
Lee Pugh
Speaking for myself, I am a disadent.
Ampere taught us that a permanent magnet supports a tangential dynamic
electrical field which is electrically clockwise as you view a south seeking
magnetic pole which is propagated radially. An adjacent magnet, having a
similar dynamic electrical field
experiences a change in the its environment and must assess the aggregate of
or modification of the electrical charge topology in which each charged
partical in motion is seeking a path of least resistance. That path changes
with the advent of outside dynamic electrical fields. The inertia of
individual partical is re-directed because those additional electrical
charges do not give the particals the elbow room they need to proceed
unaltered in course. The appearance of force having acted on the magnets
is a function which has a cause and effect.
The magnetic field observed is actually locally presented is the effect, and
the dynamic electrical fields are the cause.
I should say the specific topography of the dynamic electrical fields as
they are presented to each other is the cause.
That good ol boy, the friendly magnetic field is an apparition or illusion.
the magnetic field does not span the gap, only dynamic electrical fields do.
Re-direction of enertia is the common link to how all dedicated fields
including gravity is achieved.
Kind regards, Lee Pugh
Michael W. Hicks <som...@somewhere.net> wrote in message
news:4PDLc.7095$iK....@newsread2.news.atl.earthlink.net...
Jim Black
Let's imagine, just so we can get a simple mental picture, that the
magnets are made up of a whole bunch of little loops of wire with
current flowing through them:
[pictures designed for fixed-width font]
side front view
view
<---
__________________
/| | |
| | | |
f | | | |
r | | ^ | | | ^
o | | | current | | | | current
n | | | V | | |
t | | | |
| | | |
\| |__________________|
--->
If the loops were subject to a uniform magnetic field, the forces on
them would indeed cancel out:
side front view
view
<---
magnetic __________________
/| ----> | | |
| | | | |
| | ----> | V |
| | ^ | |force force| ^
| | ----> | |---> <---| |
| | | V | | |
| | ----> | ^ |
| | | | |
\| ----> |_________|________|
field --->
However, the magnetic field near another magnet will not be uniform.
It will be more like this:
side front view
view
_-> <---
_- magnetic __________________
/| - field | |
| | __-> | ^ |
| | -- | | |
| | ^ | | magnetic| ^
| | -----> | | <--- ---> | |
| | | V | field | |
| | --__ | | |
| | -> | V |
\| -_ |__________________|
-_ --->
->
This will result in a net force on the loop:
side front view
view
<---
force __________________
/| ---> | | |
| | | | |
| | | V |
| | ^ | |force force| ^
| | ---> | |---> <---| |
| | | V | | |
| | | ^ |
| | | | |
\| ---> |_________|________|
force --->
edA-qa mort-ora-y
> between magnetic dipoles F =A/r^3 where A is a constant of the material
> and r is the distance between the dipoles. Also, you need to times that
Where do you get this equation? No, really. I was looking for quite
some time but have been unable to find such an equation. To this point
I've been using the simple F=c/r^2 where c is the pole strenght of an
indivudal /particle/ and then integrating over the volume of the object.
But this r^3 is obviously quite different than r^2, so obviously I would
like to know whether I'm diong this correctly -- my simulations are
providing realistic results with r^2, but I am having problems in
certain areas.
--
edA-qa mort-ora-y
Idea Architect
http://disemia.com/
Igor
Well, if their dipole moments point in opposite directions, they will
repel, north facing north or south facing south. If they point in the
same direction, they will attract, north facing south or vice versa.
Joseph.D.Warner
Go to Jackson's "Classical Electrodynamics" 2nd edition. Page 178.
equation 5.41
It gives B field for a magnetic dipole. Since the Force on a dipole is
(from eq. 5.69) the del(M*B) where M is the vector dipole moment and the
B is the external magnetic field at the dipole moment (in this case B is
the B field from the other dipole) you can go and calculate the force of
one dipole on another. Then you can find the force and it is
porportional to B of one of the dipoles and B varies as 1/r^3.
Also, see eq. 5.104 that gives the vector potential for a dipole.
Remember force is the gradient of the vector potential.
I hope this helps.
Lee Pugh
Everybody should understand that anything radially propigated (like light
from a single point) must paint the annular area of increasingly sized
spheres where the point of light is in the center, with a strength which
varies inversely with the square of the radii of the individual sphere. This
is because the total light painting the complete sphere must be same
throughout individual spheres.
The strength of magnetic flux from a single pole of a magnet clearly does
not fall in that catagory and in measuring the strength I found that from a
magnetic pole no ratio holds true over a range of radii.
it is only the total of the flux that hold true and its topology
dramatically is affected by the configuration of the other pole of the same
magnet and whatever pole it is mated to for function.
Magnetic flux is a superfluid and cannot be contained uniformly. It has
attributes that suggest it can actually be in the multiple places at the
same time giving a yield in excess of its primary capability.
(during a magnetic function) A static permanent magnet has a field that
appears to be a magnetic field having lines of flux and thereby flux
density, but all a magnet really has are tangentially exhibited electrical
fields that are propigated radially. The force exhibited by any magnet is
only locally manifested and the actual magnetic field does not span the
distance to achieve action at a distance.
Kind regards, Lee Pugh
"Joseph.D.Warner" <jwa...@grc.nasa.gov> wrote in message
news:4105378B...@grc.nasa.gov...
Joseph.D.Warner
Lee Pugh wrote:
> I think this is typical of the misunderstanding of math applications,
> Everybody should understand that anything radially propigated (like light
> from a single point) must paint the annular area of increasingly sized
> spheres where the point of light is in the center, with a strength which
> varies inversely with the square of the radii of the individual sphere. This
> is because the total light painting the complete sphere must be same
> throughout individual spheres.
>
> The strength of magnetic flux from a single pole of a magnet clearly does
> not fall in that catagory and in measuring the strength I found that from a
> magnetic pole no ratio holds true over a range of radii.
That is because there are no single magnetic poles.
> it is only the total of the flux that hold true and its topology
> dramatically is affected by the configuration of the other pole of the same
> magnet and whatever pole it is mated to for function.
> Magnetic flux is a superfluid and cannot be contained uniformly. It has
> attributes that suggest it can actually be in the multiple places at the
> same time giving a yield in excess of its primary capability.
Your interpretation is your own. But as long it reproduces observables
and have dipoles whose fields fall off as 1/r^3 as you approach infinity
then it is OK.
Igor
I beg to differ. A stationary permanent magnet cannot possess any
kind of electric field, just as a stationary electric charge cannot
have a magnetic field. Put both of them in motion, however, and the
situation will change according to Maxwell's equations.