Magnetic lines of force

George Dishman wrote in message
...

"greywolf42" wrote in message
...

George Dishman wrote in message
...

{snip sections not commented on by George}

In my original post I used two filings to illustrate how
lines could be formed in a field that has no inherent
line structure.

Unfortunately, you were responding to a post about the *question* whether
there *was* an 'inherent line structure.' Your post about 'gluing' a filing
to the paper before bringing in the magnet simply confused the issue.

If you just 'drop' that first filing in place, it will always go to
one of the same lines that were traced out prior, or afterwards.

There I disagree. If you drop a single filing it
will always attach itself to the magnet if it is
free enough to move. Obviously friction usually
stops it.

The paper is held 'above' the magnet. No contact with the magnet.

Yes, my reply was misleading. I meant it would always get
as close as possible to the magnet, i.e. above the pole
on the other side of the paper.

And this is where we disagree. And why experiment is needed.

My intent was simply to
look at the formation of lines to the side of the magnet
near a line passing through the middle as in the later
diagram. Things are just simpler there and more complex
near the poles.

If you are correct, there would be no difference. It would all be 'simple.'

{snip higher levels}

I'm not talking about putting a magnet on the paper. The magnet is
UNDER
the paper. Hence you cannot get a chain of filings from one pole to the
other.

Your placing of a magnet ON the paper is a different setup. And it
doesn't
allow for the experiment to show anything.

Understood, I didn't mean to change that, sorry.

Going back to two filings with the first glued,

We never had just two filings, so we can't 'go back.'

Well I did, maybe yours fell on the carpet. Borrow
Jeff's magnet ;-) (see quotes above).

moving the magnet will not usually cause the
second to move but to rotate to remain aligned
with the field while still remaining in contact
with the first. (Try it ;-)

I don't disagree. But 'glued' filings are 'cheating.' Because it
doesn't
trace the undisturbed field of the main magnet (under the paper).

Agreed, it was intended to show that the first filing
disturbed the field in a way that would cause the
second to be preferentially attached to the first and
hence start the process of forming a line.

This doesn't address the issue under discussion -- whether the lines form
without glue.

This addresses the case of the undisturbed field:

More scientifically, suppose we have this
arrangement:

N
|
| f --
|
S

--x--

A single filing is held at 'f' and the force
plotted against the distance 'x' from the magnet
as the filing is moved along a line perpendicular
to the axis. If you were right then there should
be a cyclical variation since the force should
have maxima when the filing is on a line and
minima in-between. This is not the case.

That's because I wasn't discussing the case you have just described.
Now I understand why you wanted to 'glue' the filing to the paper.
To prevent it
from always sliding into the magnet. However, your setup does not allow
measurement of the field or field lines. To do that, one must keep the
magnet below the paper ... so that the filings will trace their patterns
without contacting the magnet. No glue is needed.

The first bit with the paper and filings was a simple
practical test most people could do at home. Jeff got
the idea and tried it. It is illustrative only.

But it is not 'illustrative' of the issue under discussion. People can do
the experiment without glue and without placing the magnet on top of the
paper.

The final "More scientifically" paragraph is perhaps the
one we should look at if you still think that the lines
are part of the field rather than an artefact caused by
their distortion of the field. I had intended that this
be done without any paper but if you prefer imagine the
filing suspended above the magnet on a fine thread and
the force measured by attaching the other end of the
thread to a balance.

I'm *not* referring to levitation or "without any paper." Suspend paper in
air (not filings) over magnet. Use one hand or a sheet of smooth plastic
instead of paper. Drop the filings onto the paper. If I am right, the
filings will always trace out the same pattern, when the paper is held at
the same location. The patterns will be random if you are right.

I'm sure you can think of other
ways to do this but the aim is simple - avoid errors due
to friction and other outside influences.

You still haven't grasped the essence of the experiment.

Assuming you accept this or come up with your own
experimental technique, do you think there would be a
periodic variation of force as a function of distance
that would result in lines?

Please try the experiment, first. If you are interested in theory, go read
Faraday's work.

greywolf42
ubi dubium ibi libertas

"greywolf42" wrote in message
...
George Dishman wrote in message
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"greywolf42" wrote in message
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George Dishman wrote in message
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Snip everything about a glued-down filing, it seems to
have caused more confusion than it removed.

More scientifically, suppose we have this
arrangement:

N
|
| f --
|
S

--x--

A single filing is held at 'f' and the force
plotted against the distance 'x' from the magnet
as the filing is moved along a line perpendicular
to the axis. If you were right then there should
be a cyclical variation since the force should
have maxima when the filing is on a line and
minima in-between. This is not the case.

Snip more on the glued filing.

The final "More scientifically" paragraph is perhaps the
one we should look at if you still think that the lines
are part of the field rather than an artefact caused by
their distortion of the field. I had intended that this
be done without any paper but if you prefer imagine the
filing suspended above the magnet on a fine thread and
the force measured by attaching the other end of the
thread to a balance.

I'm *not* referring to levitation or "without any paper."

Nor am I, I am suggesting a method for measuring the
field without any errors caused by friction of filings
on the paper and without the distortion caused by
having multiple filings. Remember Jeff's original
question:

[Jeff root wrote:]
Could you apply this same kind of wonderfully clear exegesis to
the term "magnetic lines of force"? I keep seeing intimations
that they have some kind of reality. Thank you!

I understand him to be asking 'are the lines formed in
the filings indicative of real lines in the field'.

Suspend paper in
air (not filings) over magnet. Use one hand or a sheet of smooth plastic
instead of paper. Drop the filings onto the paper. If I am right, the
filings will always trace out the same pattern, when the paper is held at
the same location. The patterns will be random if you are right.

No, if I am right the filings will also always trace
out a pattern of lines but not because there are lines
of greater strength inherently in the field, it is
because the first filing causes a distortion which
influences where the second goes and so on. I expect
the pattern to be the same each time if the same
quantity and size of filings is used and all other
parameters are also held constant (strength of magnet,
distance from paper etc.) given enough motion of the
paper to make friction inconsequential.

I'm sure you can think of other
ways to do this but the aim is simple - avoid errors due
to friction and other outside influences.

You still haven't grasped the essence of the experiment.

I think you haven't grasped the essence of Jeff's
question: are the lines formed in the filings
indicative of 'real' lines in the field? My answer
was no, the lines are formed as a consequence of the
distortion produced by the presence of the filings
themselves.

Please try the experiment, first.

I did it many times as a child. To falsify my answer,
the appropriate experiment is to measure the field
without the filings. If I am wrong, preferred lines
will still be present.

If you are interested in theory, go read
Faraday's work.

Been there, done that (30 years ago), would have to
look it up again :-( I'm sure it says the field of
a dipole reduces monotonically with distance from
the magnet.

George

George Dishman wrote in message
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"greywolf42" wrote in message
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George Dishman wrote in message
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"greywolf42" wrote in message
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George Dishman wrote in message
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{finishing the snip about glued filings}

The final "More scientifically" paragraph is perhaps the
one we should look at if you still think that the lines
are part of the field rather than an artefact caused by
their distortion of the field. I had intended that this
be done without any paper but if you prefer imagine the
filing suspended above the magnet on a fine thread and
the force measured by attaching the other end of the
thread to a balance.

I'm *not* referring to levitation or "without any paper."

Nor am I, I am suggesting a method for measuring the
field without any errors caused by friction of filings
on the paper and without the distortion caused by
having multiple filings. Remember Jeff's original
question:

[Jeff root wrote:]
Could you apply this same kind of wonderfully clear exegesis to
the term "magnetic lines of force"? I keep seeing intimations
that they have some kind of reality. Thank you!

I understand him to be asking 'are the lines formed in
the filings indicative of real lines in the field'.

And I understand him to be asking 'are the lines formed in the filings
real?' A 'field' is not 'real'. It is a mathematical device. Useful, but
not physical -- or 'real.' If you try to make 'reality' in a fiction (the
field), you are going to fail.

Suspend paper in
air (not filings) over magnet. Use one hand or a sheet of smooth
plastic
instead of paper. Drop the filings onto the paper. If I am right, the
filings will always trace out the same pattern, when the paper is held
at
the same location. The patterns will be random if you are right.

No, if I am right the filings will also always trace
out a pattern of lines but not because there are lines
of greater strength inherently in the field,

Here you have reversed Jeff's question. Instead of addressing the 'reality'
of the lines of force, you have subsumed your entire argument to the
mathematical fiction of the 'field.'

it is
because the first filing causes a distortion which
influences where the second goes and so on. I expect
the pattern to be the same each time if the same
quantity and size of filings is used and all other
parameters are also held constant (strength of magnet,
distance from paper etc.) given enough motion of the
paper to make friction inconsequential.

In which case you don't have a scientific theory -- for it can't be
disproved. If there can be no discrimination between 'real' forces causing
the 'same pattern' and 'secondary distortions' causing the 'same pattern.'

However, there is a way out. For there is no need, if I am correct, for the
quantity of filings to be held constant.

I'm sure you can think of other
ways to do this but the aim is simple - avoid errors due
to friction and other outside influences.

You still haven't grasped the essence of the experiment.

I think you haven't grasped the essence of Jeff's
question: are the lines formed in the filings
indicative of 'real' lines in the field? My answer
was no, the lines are formed as a consequence of the
distortion produced by the presence of the filings
themselves.

Again, as soon as you mentioned 'lines in the *field*', you show that you
don't grasp what *I* see as the essence of Jeff's question. Which is
simply, 'are the line real?' There is no need to drag in a mathematical
fiction, and then argue about the fiction.

Please try the experiment, first.

I did it many times as a child. To falsify my answer,
the appropriate experiment is to measure the field
without the filings. If I am wrong, preferred lines
will still be present.

The *field* has nothing to do with Jeff's question. Fields cannot be
measured without test particles (filings). You have just insultated your
theory from disproof.

If you are interested in theory, go read
Faraday's work.

Been there, done that (30 years ago), would have to
look it up again :-( I'm sure it says the field of
a dipole reduces monotonically with distance from
the magnet.

Again, we're discussing 'lines of force' (Faraday's words), not *fields*
(invented by Maxwell and Heaviside).

greywolf42
ubi dubium ibi libertas

"greywolf42" wrote in message
...

George Dishman wrote in message
...

{finishing the snip about glued filings}

The bit left wasn't about the glued filing explanation. I'll
put it back later. In the meantime I'll snip a lot regarding
Jeff's question. Perhaps he will enlighten us if he reads this.

[Jeff root wrote:]
Could you apply this same kind of wonderfully clear exegesis to
the term "magnetic lines of force"? I keep seeing intimations
that they have some kind of reality. Thank you!

I understand him to be asking 'are the lines formed in
the filings indicative of real lines in the field'.

And I understand him to be asking 'are the lines formed in the filings
real?'

I am sure Jeff is familiar with the experiment, however,
we cannot resolve that without Jeff's help.

No, if I am right the filings will also always trace
out a pattern of lines but not because there are lines
of greater strength inherently in the field,
snip more on the question
it is
because the first filing causes a distortion which
influences where the second goes and so on. I expect
the pattern to be the same each time if the same
quantity and size of filings is used and all other
parameters are also held constant (strength of magnet,
distance from paper etc.) given enough motion of the
paper to make friction inconsequential.

In which case you don't have a scientific theory -- for it can't be
disproved.

See below.

If there can be no discrimination between 'real' forces causing
the 'same pattern' and 'secondary distortions' causing the 'same pattern.'

However, there is a way out. For there is no need, if I am correct, for
the
quantity of filings to be held constant.

snip
The *field* has nothing to do with Jeff's question. Fields cannot be
measured without test particles (filings). You have just insultated your
theory from disproof.

Not at all, the bit you snipped was a method for resolving
the debate:

[I wrote:]
More scientifically, suppose we have this
arrangement:

N
|
| f --
|
S

--x--

A single filing is held at 'f' and the force
plotted against the distance 'x' from the magnet
as the filing is moved along a line perpendicular
to the axis. If you were right then there should
be a cyclical variation since the force should
have maxima when the filing is on a line and
minima in-between. This is not the case.

The two propositions can be tested by measuring the force
on a single filing and looking for evidence of lines in
the plot of force versus distance.

This is entirely independent of whether "the field is real"
or not, so neither of our opinions on that matter.

George

George Dishman wrote in message
...

"greywolf42" wrote in message
...

George Dishman wrote in message
...

{finishing the snip about glued filings}

The bit left wasn't about the glued filing explanation. I'll
put it back later.

Sure it was. The "single filing is held at 'f'" is a glued filing. (That's
what's 'holding' it.) And if you 'glue' it at different places, it's still
'glue.' (It's not the 'glue' that's important -- but the arbitrary 'holding'
of a filing at random points.)


In the meantime I'll snip a lot regarding
Jeff's question. Perhaps he will enlighten us if he reads this.

[Jeff root wrote:]
Could you apply this same kind of wonderfully clear exegesis to
the term "magnetic lines of force"? I keep seeing intimations
that they have some kind of reality. Thank you!

I understand him to be asking 'are the lines formed in
the filings indicative of real lines in the field'.

And I understand him to be asking 'are the lines formed in the filings
real?' A 'field' is not 'real'. It is a mathematical device. Useful,
but
not physical -- or 'real.' If you try to make 'reality' in a fiction
(the
field), you are going to fail.

I am sure Jeff is familiar with the experiment, however,
we cannot resolve that without Jeff's help.

Did you have a substantive comment to make?

No, if I am right the filings will also always trace
out a pattern of lines but not because there are lines
of greater strength inherently in the field,
snip more on the question
it is
because the first filing causes a distortion which
influences where the second goes and so on. I expect
the pattern to be the same each time if the same
quantity and size of filings is used and all other
parameters are also held constant (strength of magnet,
distance from paper etc.) given enough motion of the
paper to make friction inconsequential.

In which case you don't have a scientific theory -- for it can't be
disproved.

See below.

If there can be no discrimination between 'real' forces causing
the 'same pattern' and 'secondary distortions' causing the 'same
pattern.'

However, there is a way out. For there is no need, if I am correct, for
the
quantity of filings to be held constant.

snip
The *field* has nothing to do with Jeff's question. Fields cannot be
measured without test particles (filings). You have just insultated
your
theory from disproof.

Not at all, the bit you snipped was a method for resolving
the debate:

[I wrote:]
More scientifically, suppose we have this
arrangement:

N
|
| f --
|
S

--x--

A single filing is held at 'f' and the force
plotted against the distance 'x' from the magnet
as the filing is moved along a line perpendicular
to the axis. If you were right then there should
be a cyclical variation since the force should
have maxima when the filing is on a line and
minima in-between. This is not the case.

The two propositions can be tested by measuring the force
on a single filing and looking for evidence of lines in
the plot of force versus distance.

'Measuring the force on a single filing' requires 'gluing' a filing. Again,
it's not the 'glue' that's important -- but the arbitrary 'holding' of a
filing at random points. The physical constraint on the particle is a real,
physical limitation.

This is entirely independent of whether "the field is real"
or not, so neither of our opinions on that matter.

That's why we do experiments.

greywolf42
ubi dubium ibi libertas

"greywolf42" wrote in message
...

George Dishman wrote in message
...

"greywolf42" wrote in message
...

George Dishman wrote in message
...

{finishing the snip about glued filings}

The bit left wasn't about the glued filing explanation. I'll
put it back later.

Sure it was.

No it wasn't. I wrote it so I should know! The earlier
part of the email was about a glued filing, this was not.

The "single filing is held at 'f'" is a glued filing. (That's
what's 'holding' it.)

A single filing is held at 'f' and the force
plotted against the distance 'x' from the magnet
as the filing is moved along a line perpendicular
to the axis.

I had envisaged the filing perhaps being suspended from
a balance by a fine thread but I left it unspecified as
I expected you to use anything I suggested as an excuse
to nitpick and avoid the real point. Obviously it wasn't
glued since it could not then be "moved along a line
perpendicular to the axis".

And if you 'glue' it at different places, it's still
'glue.' (It's not the 'glue' that's important -- but the arbitrary
'holding'
of a filing at random points.)

No, what was important was the measurement of the force
without other magnetic influences and its relationship
to distance.

In the meantime I'll snip a lot regarding
Jeff's question. Perhaps he will enlighten us if he reads this.

[Jeff root wrote:]
Could you apply this same kind of wonderfully clear exegesis to
the term "magnetic lines of force"? I keep seeing intimations
that they have some kind of reality. Thank you!

I understand him to be asking 'are the lines formed in
the filings indicative of real lines in the field'.

And I understand him to be asking 'are the lines formed in the filings
real?' A 'field' is not 'real'. It is a mathematical device.
Useful,
but
not physical -- or 'real.' If you try to make 'reality' in a fiction
(the
field), you are going to fail.

I am sure Jeff is familiar with the experiment, however,
we cannot resolve that without Jeff's help.

Did you have a substantive comment to make?

Let me make it clearer for you. I understand your view
of what Jeff was asking, and I think you understand mine.
The only way to resolve that difference of opinion is for
Jeff to say what he meant because only Jeff knows what he
intended.

If you were referring to your comments on 'reality', I
think that best left to philosophy groups. This group
is in the "sci." hierarchy.

[I wrote:]
More scientifically, suppose we have this
arrangement:

N
|
| f --
|
S

--x--

A single filing is held at 'f' and the force
plotted against the distance 'x' from the magnet
as the filing is moved along a line perpendicular
to the axis. If you were right then there should
be a cyclical variation since the force should
have maxima when the filing is on a line and
minima in-between. This is not the case.

The two propositions can be tested by measuring the force
on a single filing and looking for evidence of lines in
the plot of force versus distance.

'Measuring the force on a single filing' requires 'gluing' a filing.

There are many ways it could be measured. I suggested
above attaching it by a thread to a balance but I'm sure
you can think of others. Gluing it to the piece of paper
would certainly not be my first choice.

Again,
it's not the 'glue' that's important -- but the arbitrary 'holding' of a
filing at random points. The physical constraint on the particle is a
real,
physical limitation.

What is important is whether there is evidence for "lines"
in the plot of force versus distance because this technique
removes the possibility that the influence of other filings
is the cause. If evidence for lines appeared in the graph,
I would be wrong and you would be right. It's as simple as
that.

George

"Asimov" replied to Jeff Root:

When I've played with iron filings and magnets in the past,
the effect of friction between the filings and paper has always
seemed obvious. I'm not sure that I would learn anything from
using a low-friction surface instead (what seemed obvious might
not even be real), but I'll try it if I can. Do you have any
suggestions for a low-friction material to put between the
filings and the magnet?

Yes try to place the iron filings in a bottle filled with oil or
water. Then shake it so they are all in suspension then try your
magnets.

Good suggestion. I happen to have a small bottle of olive oil,
the taste of which I didn't like. (According to some opinions,
it probably went rancid while in my care, however, I'm pretty
sure the taste did not change markedly after I opened it.) The
bottle has flat sides, ideal for the task.

The filings are now in the bottle. I find that their motion is
significantly different, but mostly due to the viscosity of the
oil. It doesn't seem to make any difference at all to how the
filings clump, or the appearance of "lines".

I've dumped the oil and filings into a white ceramic bowl with
a flat bottom. Easier to see the filings, but impossible to
see exactly where the magnet is.

-- Jeff, in Minneapolis

..

George Dishman replied to Jeff Root:

The shape of the filings is obviously significant. Do you have
any suggestions for getting filings which are nearly spherical,
and which are not themselves magnetized? Maybe a particular
kind of iron or steel?

No, but I would use thin pointy ones anyway so they show the
direction of the field.

Without an enormous effort to sort them out, I will take what
I get from filing. The filings are too small to make out very
well with a 30-power magnifier, but they appear to be fairly
uniform in size, and random in shape. No long, thin, pointy
ones at all, though. But little random globs clinging together
give the appearance of long, thin, pointy needles.

Just now I filed a nail with two different sizes of file. The
bigger, slightly coarser file gave bigger filings, but it isn't
clear that the size and shape distribution is different.

That was an editing error. It isn't clear that the shape
distribution is different, because my magnifier isn't powerful
enough for me to see the shapes easily. The finer file did
definitely give smaller filings, and the coarser file gave
larger filings.

I made the filings onto a hard plastic tray from the kitchen.
It seems to have lower friction than some paper. When I apply
a magnet, the itty-bitty little filings climb up on each other's
shoulders to do a flea-circus stunt where they make relatively
huge needles (compared to the size of the filings) which stand
up from the tray surface.

With just a single filing, is there any evidence of
preferred locations that it wants to go to?

That has turned out to be a very hard question to answer.
I think a proper answer might require more thorough examination
of the setup and careful measurement of the observations than I
want to bother with.

Filings in water in a thin, transparent, styrene tray are
noticeably retarded by friction with the tray surface. Filings
floating on the surface of that water move freely. A floating
filing goes to a point over the magnet. When I move the magnet,
careful to keep the orientation unchanged, the filing stays in
the same position relative to the magnet. That is what I would
expect, lines or no lines. However, the coupling between the
magnet and filing is loose, not tight. the filing will slosh
back and forth with the water while being held by the magnet.

Some factors seen to affect motion or positioning of filings:

- Number of filings
- Friction between the filing(s) and the surface
- Shape of the magnet
- Orientation of the magnet
- Changing the orientation of the magnet
- Changing the direction of motion of the magnet

The most remarkable effect is clumping of the filings into
well-separated stacks. When filings stand up on the surface,
they may all be in one clump, or in many separate clumps which
are fairly evenly-spaced. Larger clumps tend to be spaced
farther apart from each other. Moving the magnet away tends
to make clumps move apart.

Some orientations and directions of motion of the magnet lead
to a single large clump; other orientations and motions lead
to many small clumps which often look like a hedgehog.

Most tellingly, perhaps, some orientations and directions of
motion of the magnet give a really neat circulation pattern of
the clumps, rather than a simple linear motion.

-- Jeff, in Minneapolis

..

"greywolf42" replied to George Dishman:

In my original post I used two filings to illustrate how
lines could be formed in a field that has no inherent
line structure.

Unfortunately, you were responding to a post about the
*question* whether there *was* an 'inherent line structure.'
Your post about 'gluing' a filing to the paper before bringing
in the magnet simply confused the issue.

It didn't confuse me. However, I interpreted the proceedure
George described to be that the filing was glued down after it
had settled into alignment with the magnet, not before. His
post was not explicit, but the implication was so obvious that
it hadn't occurred to me to interpret it the way you did.

But it is not 'illustrative' of the issue under discussion.
People can do the experiment without glue and without placing
the magnet on top of the paper.

The fact that you thought George was saying to put the magnet
on the same side of the paper as the filings-- and you repeated
that error in another post-- shows that your comprehension
isn't necessarily as good as you think it is.

The demonstration with a glued-down filing could be very
useful if carefully done. It would show exactly what George
intended it to show: The effect of one filing on another.
That wouldn't be possible if one filing were not glued down.

-- Jeff, in Minneapolis

..

George Dishman replied to "greywolf42":

[Jeff root wrote:]
Could you apply this same kind of wonderfully clear exegesis to
the term "magnetic lines of force"? I keep seeing intimations
that they have some kind of reality. Thank you!

I understand him to be asking 'are the lines formed in
the filings indicative of real lines in the field'.
...
I think you haven't grasped the essence of Jeff's question:
are the lines formed in the filings indicative of 'real'
lines in the field? My answer was no, the lines are formed
as a consequence of the distortion produced by the presence
of the filings themselves.

"greywolf42" replied to George Dishman:

And I understand him to be asking 'are the lines formed in the
filings real?' A 'field' is not 'real'. It is a mathematical
device. Useful, but not physical -- or 'real.' If you try to
make 'reality' in a fiction (the field), you are going to fail.

The magnetic field is obviously real. I see its effect on iron
filings. I see its effect on a magnetic compass. I feel its
effect when I hold a magnet near a large piece of iron or steel.

My question had nothing to do with filings, only with "magnetic
lines of force", whatever those are supposed to be. I know what
magnets are; I have a pretty good idea what magnetism is; I know
what lines are; I know what forces are. I'm not certain what
"magnetic lines of force" are.

My question was specifically directed to George Dishman. I was
sure he would understand my question as I worded it, and he did.
However, it was worded in such a way that one pretty much needed
to know the answer in order to understand the question. It is
hard to word it in such a way as to be clear to someone who
doesn't already know what I mean, and how I have been confused
by other peoples' use of the term "magnetic lines of force".

I have read descriptions of "magnetic lines of force" in which
an analogy was drawn to lines of latitude or longitude, or to
lines of elevation on a topographic map. Those struck me as
awfully poor analogies. The directions of those lines are
nothing like the directions of the force vectors in a magnetic
field. If anything, lines of elevation are at a right angle
to the direction that analogous lines of force should be.

But I sometimes come across a text in which the "lines" in a
magnetic field are talked about in a way which implies that
they are more than just lines showing the direction of the
force vector. I don't understand that, and that is what I
was asking about.

George Dishman wrote:

What is important is whether there is evidence for "lines"
in the plot of force versus distance

Not knowing what is supposed to be meant by the expression
"magnetic lines of force", I didn't assume that the force
measured on a line would be different from the force measured
between lines. The lines could be there, perfectly real, but
not make any difference in the force, for all I knew.

Also, I wouldn't assume that individual lines, if they existed,
could be detected by *any* means, just as it is not possible to
detect individual photons of radio waves.

-- Jeff, in Minneapolis

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