Interesting Simple Magnetic Force Question

WBahn

Joined Mar 31, 2012
29,976
Hi,

Yes thanks, that helps to clarify the right hand rule problem, which i am now going to call Problem #1. That works with the original wire and field i posted in the first post (wire along x, conventional current left to right along x, B field into the page).

Problem #2 comes in when we try to do the cross product. As i was saying before, the cross of two vectors U and V where they are:
U=[1,0,0] (wire length with conventional current flow)
V=[0,0,1] (mag field B)

and the cross product of U and V:
U x V = [0,-1,0]

shows a force oriented DOWN not UP as the right hand rule shows.
I think what you are missing is that 3-D Cartesian coordinate systems themselves are either right-handed or left-handed. If the coordinates are of the form <x,y,z>, the to be right-handed it must be true that:

<1,0,0> x <0,1,0> = <0,0,1>

Your U vector is in the positive X direction, which you have defined as being left to right in the plane of the page. Your V vector is in the positive Z direction, which you have defined as being downward into the page. In order for this to be a right-handed coordinate system, your positive Y direction MUST go downward in the plane of the page. Thus, the vector [0,-1,0] is pointing upward in the plane of the page.
 

Thread Starter

MrAl

Joined Jun 17, 2014
11,389
I think what you are missing is that 3-D Cartesian coordinate systems themselves are either right-handed or left-handed. If the coordinates are of the form <x,y,z>, the to be right-handed it must be true that:

<1,0,0> x <0,1,0> = <0,0,1>

Your U vector is in the positive X direction, which you have defined as being left to right in the plane of the page. Your V vector is in the positive Z direction, which you have defined as being downward into the page. In order for this to be a right-handed coordinate system, your positive Y direction MUST go downward in the plane of the page. Thus, the vector [0,-1,0] is pointing upward in the plane of the page.
Hi,

I think you may be on to something here, but when i checked Wolfram they show the coordinate system as i indicated as a right hand coordinate system. They show it with x to the right, y to the left, and z going straight up. If rotated so that z points out of the page (as i suggested as being 'standard position') then x is to the right, y straight up, and z out of the page, as i had assumed, and all the axises have the same relative orientation.
Any ideas what is happening here?
 

WBahn

Joined Mar 31, 2012
29,976
Hi,

I think you may be on to something here, but when i checked Wolfram they show the coordinate system as i indicated as a right hand coordinate system. They show it with x to the right, y to the left, and z going straight up. If rotated so that z points out of the page (as i suggested as being 'standard position') then x is to the right, y straight up, and z out of the page, as i had assumed, and all the axises have the same relative orientation.
Any ideas what is happening here?
I don't know what you mean by "x to the right, y to the left".

The system x to the right, y straight up, z out of the page is right-handed.
 

Thread Starter

MrAl

Joined Jun 17, 2014
11,389
I don't know what you mean by "x to the right, y to the left".

The system x to the right, y straight up, z out of the page is right-handed.
Hi,

Yes i agree, so that would suggest that if B was into the page, it was along the -z axis right?
That would mean something has to be made negative right?

Here's a quick screen shot of a right handed coord system. In my original question, B is along the -z axis.
 

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WBahn

Joined Mar 31, 2012
29,976
Yes, in your original diagram if the current was in the +x direction (to the right) and the field was into the page, then the most conventional assignment would be that it is in the -z direction (and for the +y axis to be toward the top of the page).

So your current unit vector is <1,0,0> and your magnetic field unit vector is <0,0,-1> making your force unit vector

<1,0,0> x <0,0,-1> = <0,1,0>

Also, in your diagram above, the convention is for the arrowhead on an axis to point in the positive direction for that axis.
 

Lool

Joined May 8, 2013
116
This is the first time I ever heard of the right hand rule being ambiguous. If it seems ambiguous, then you are not applying the rule correctly, or you are using the wrong formula with B x A used in place of A x B.

Ambiguity creeps in only if you cant remember whether you are supposed to use the right hand rule or the left hand rule, but most people are right handed and we usually use right handed coordinate systems, so you should not get that part wrong.
 

WBahn

Joined Mar 31, 2012
29,976
This is the first time I ever heard of the right hand rule being ambiguous. If it seems ambiguous, then you are not applying the rule correctly, or you are using the wrong formula with B x A used in place of A x B.

Ambiguity creeps in only if you cant remember whether you are supposed to use the right hand rule or the left hand rule, but most people are right handed and we usually use right handed coordinate systems, so you should not get that part wrong.
I think the problem comes, when finding the direction of C = A x B, from the common method of pointing the index finger along A, the middle finger along B, and the thumb along C. They forget whether the index finger points along A or B. This is why I prefer the method of using all of the fingers as (or just the index finger, same thing) to first point along A and then cross it over toward B.
 

Thread Starter

MrAl

Joined Jun 17, 2014
11,389
Hi again,

I have to agree totally. The word shouldnt really be "ambiguous", it should be just a little "confusion" of which finger to use for what. If you look around the web, you'll see two variations both claiming to be correct. They swap the index and middle fingers. Only one can be right. It's not even about left or right hand really, although i could see problems there too :)
But there are other things left out of the picture too though. One is that the type of current has to be specified. Is it a positive charge or a negative charge? The usual physics book explanation states that the definition uses the positive charge for the Lorentz formula, and this boils down to conventional current flow when we get to the I*L x B formula for whole wires. So even drawing the 'hand' with the fingers pointing (some funny drawings on the web) is not really enough unless the type of current is specified, but really it should be conventional current to keep up with the text book norms i think.

Then when we get to the experimental part, we have to be aware of the direction of B relative to the North and South poles. When we get to the cross product, we have to know what coordinate system we are dealing with and get the right one.

So it's not that anything is really ambiguous, it just appears to be ambiguous sometimes because not everything is specified at the time of writing of many articles on this subject. That is, some little details are left out. One thing i notice though, is that in general the more educated the author is the more tendency there is to include these details. For example, one writer/experimenter makes it very hard to figure out what lead is positive and which is negative, which means we cant deduce anything from that experiment, while the other makes it very clear which lead is positive and what pole is north and which south, etc.

Let me give a quick example...
Say i do an experiment like this and i state:
"When i apply the current, the wire moves out from between the two magnets, thus proving the Lorentz law".
See what i mean? Yes it is true, very true and completely correct, but there are too many details left out. We dont know which way the current was flowing, we dont know where the pole faces were, all we know is that a force in some direction has been observed because current was flowing in the wire and the wire was in a magnetic field.
If we replaced the wire with a sub atomic particle, we would not be able to tell if it was a proton or an electron unless someone who was present at the time of the experiment was told and could report that to us too :)
 

BillO

Joined Nov 24, 2008
999
Does this help?

Reading this I feel most are getting tripped up by math they can't relate to the physical situation. This diagram puts it into perspective of the physics.

force-on-wire.jpg

In this diagram, the current flow is away from the viewer. Making the appropriate rotations to align this to the original question would imply that the answer to that question is, the force on the wire will be up.
 
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BR-549

Joined Sep 22, 2013
4,928
We have two kinds of current flow. Which one are you using?

Magnetic lines traveling in the same direction, attract, and magnetic lines traveling in opposite directions repel.
 

BillO

Joined Nov 24, 2008
999
We have two kinds of current flow. Which one are you using?
What are you talking about? I stated the conditions. Current flow away from the viewer. Of course that would be conventional current flow, otherwise I would hsve mentioned it.

Magnetic lines traveling in the same direction, attract, and magnetic lines traveling in opposite directions repel.
Okay, wrong, but what does that have to do with it anyway?

Magnetic field lines are not the field, only an imaginary indicator of the density and direction of the field. Those going in the same direction add, those going in opposite direction subtract. This is a way to represent the resulting changes in field density.

In the depicted situation, which I think a child could see, the field around the wire increases the overall field density above the wire and lowers it below the wire creating a gradient toward the low side.
 

Thread Starter

MrAl

Joined Jun 17, 2014
11,389
Does this help?

Reading this I feel most are getting tripped up by math they can't relate to the physical situation. This diagram puts it into perspective of the physics.

View attachment 91442

In this diagram, the current flow is away from the viewer. Making the appropriate rotations to align this to the original question would imply that the answer to that question is, the force on the wire will be up.
Hi,

Yes nice diagrams which points out MOST of the required details.

However, if you read my posts before this you would see that i also pointed out that the type of current flow needs to be included in the description too. The reason for this is because in a lot of physics electron flow is used as well as conventional current flow, therefore to nail everything down so there is never another argument the current flow type needs to be shown too.
You'll notice that in the best experiments they always show the polarity of the battery supply so that you can trace the current flow by looking at what end of the 'wire' the positive battery terminal is connected to. This shows us that if we follow the positive direction current starting from the positive terminal (usually the red one) through the wire we eventually reach the magnet(s) and then we can relate the current flow to the whole experiment as well as the direction of the magnetic field if the poles are marked as nicely shown in your diagram.
So all of the issues are:
1. Where is the north pole and south pole relative to the wire, and thus the field direction.
2. The field is considered to be directed from the south pole to the north pole.
3. Which way is the current flowing in the wire, and is that direction relative to conventional current or to electron current flow, or alternately what battery polarities are the two ends of the wire connected to.
4. Which direction did the wire move toward.
5. For using the cross product, are the axises lined up according to the right handed coordinate system or not. For simplicity, conventional current along x toward +x, B field along z toward +z, and force along y toward +y.

Leaving anything out means we have to guess, and after looking on the web and seeing so many mistakes we dont want to have to guess if the author meant conventional or electron current flow.
For example, we can find sites with two of the fingers swapped, but if we also swap the type of current flow (electron flow instead of conventional current flow) then it still works out right, but if we didnt know that it would give us the wrong answer (wrong deflection direction).
 

BR-549

Joined Sep 22, 2013
4,928
Billo, I guess it’s the way we are taught. Of course conventional flow and real flow are just inverts, but I need to know which one you are starting with.

Saying current flows into the paper, without knowing if you are stating conventional or real, doesn’t give me the true reference direction of flow. i.e....the direction of real current.

And I did transpose the magnetic relationship.

The two poles(north and south) of the stationary field are clearly indicated on your illustrations.

Your current is now clear also.

I hope that we are all agreed that the stationary magnetic field is interacting with the magnetic field of the conductor, right?

And that we can change the direction of conductor movement by reversing the stationary B poles OR by changing the direction of current flow.....right?

We should all be on this page now.

My point is this.

WHERE are the magnetic poles for the conductor? After all, this is what is interacting with the stationary B poles.

The magnetic poles of a conductor are always in the center of the loop the the conductor is part of.

So................if we physically flip the position of the loop, keeping the conductor part where it is, relative the the stationary B field, the direction of conductor movement will change but the current will not.
 

BillO

Joined Nov 24, 2008
999
The magnetic poles of a conductor are always in the center of the loop the the conductor is part of.

So................if we physically flip the position of the loop, keeping the conductor part where it is, relative the the stationary B field, the direction of conductor movement will change but the current will not.
In this ideal case there are no such poles. In any real experiment, the poles you speak of would be extremely weak and very far from the situation (or event, if you prefer) of the experiment and would have vanishingly little effect on the outcome as they would be a comparatively large distance outside the field between the magnets. The only field due to the current through the wire we need concern ourselves with is the circular field about the wire. The experiment is ridiculously easy to set up. Try it and see.
 
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Thread Starter

MrAl

Joined Jun 17, 2014
11,389
In this ideal case there are no such poles. In any real experiment, the poles you speak of would be extremely weak and very far from the situation (or event, if you prefer) of the experiment and would have vanishingly little effect on the outcome as they would be a comparatively large distance outside the field between the magnets. The only field due to the current through the wire we need concern ourselves with is the circular field about the wire. The experiment is ridiculously easy to set up. Try it and see.
Hi,

Sorry but you misquoted those comments because they did not come from me they came from BR549 :) See post #35.

BR549:
I suppose you can look at the field of the wire. The direction of that field should tell you which way the wire will travel. But in reality the existing B field acts on the particles in the wire, and the particles are bound to the wire atomic structure so the whole wire moves. I am not sure how much it matters though which way you look at it. The baseline theory comes from the Lorentz formula though and before it evolves into the 'wire' formula it deals with particles. After an integration it then becomes the 'wire' formula and so the particles statistically meld into the current.
Looking at the total current view it looks like the side of the wire that has the same orientation as the field gets pushed and the other side gets pulled.
That would be the same case for two magnets where the like poles push and the unlike poles pull.
 
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Thread Starter

MrAl

Joined Jun 17, 2014
11,389
Hi again,

Thanks, i hate saying things i didnt say (chuckle).

But you want a really good laugh? Wait till you hear this.

There is still a discrepancy in the way we were associating the magnet poles and the direction of the B field. I checked some more reliable sources and found the opposite of what we were assuming so far. It turns out that the B field in physics is considered to be running from the NORTH pole to the SOUTH pole...not the other way around. This can only mean that experiments on the web that i found had marked their magnets wrong.

Since there are so many references that say one way and more that say the other way, the only way to be sure was to do an experiment.

EXPERIMENT (see attachment)

Using a CRT oscilloscope with the sweep set to use an external Horizontal input and with that Horizontal input at zero, a small bright dot appears in the middle of the screen. Using the position control the dot is moved to the left slightly so it is closer to one side of the scope body. As a side note, the electrostatic field causes the dot to move to the left side, but we are not concerned with that right now.
So the dot sits at the 0v line near the left side of the screen.
Next, a magnet is introduced near the left side of the scope body, with the NORTH pole facing the left side of the CRT screen and thus the dot, and that means the particles that zoom toward the screen get acted upon by the magnetic field of the newly introduced magnet, by its north pole.
As it turns out, the beam of electrons is deflected DOWN, not up as we would have expected had we believed the two experiments on the web.

To explain the defection, we can look at the diagrams in the attachment. In the upper right we see the coordinate system with a conventional current flow I (positive particles) and a B field directed out of the page. The resulting force is downward. There seems to be no doubt about this now.

If we rotate that system so that the B field aligns with the B field shown for the scope which is right to left, that means the current vector I (green) points out of the page. The force still points down however. So everything would be just wonderful, except for one detail: the current in the CRT scope is made up of negative particles, which means we have to reverse the force. That means if we follow the south to north B field direction convention then the particle moved the wrong way :)
If we follow the north to south B field direction convention then the particle did what it should have done, it moved down.
BTW, the magnet was tested beforehand by suspending it on a long thread and waiting for its direction to settle making sure there was little torque on the thread. Then, applying a small amount of torque, the magnet does not rotate. This means it is aligned with the earths field and pretty stable. The face of the magnet that points toward the north is called the North Pole.

This is what i mean by 'skewed'. We have several things mixed up now from the web at large:
1. Type of current (conventional or electron flow)
2. Which finger points in the direction of the current, which along B.
3. The direction of the B field relative to the magnet.

In any case, it was an interesting experiment, and no wires needed. BTW all the references state that the north seeking pole of the magnet is to be labeled "North". That's about the only thing they all agree upon :)

NOTE:
In the attachment, the dot at the zero line (#1) is the dot when there is no magnet near the scope body. The dot under the zero line (#2) is where it moved when the magnet was brought near the body of the scope.

IMPORTANT NOTE:
The B field arrow shown in the drawing is the assumed B field which is now believed to be backwards (because of the South to North B field direction mixup). If this is reversed, then the downward motion of the beam is explained perfectly.

More comments/ideas welcome.
 

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BR-549

Joined Sep 22, 2013
4,928
MrAl,

I believe that nature does not use a point as a reference.

I think it uses rotation. I believe rotation sets the angle and direction of dimension.

Which side of the rotation you are on. Left or right. In or out. The in and out happens in both planes just like the left and right.

Current is different from independent charge movement.

If you can detect the electron or proton in the magnetic field, it should be quite easy to tell the difference.

The electron should move much faster.

Also, one should rotate or spiral in one direction and the other, rotate or spiral the other direction.
 
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