# Imaginary Field Lines vs True Iron Filings

1. Sep 23, 2010

### Ralph Spencer

My (high school, gah!) text book gives an experiment: I take a straight current carrying conductor, a cardboard sheet is placed perpendicular to the conductor, so that the conductor passes straight through the sheet, remains perpendicular. Then I use a salt sprinkler to sprinkle iron filings on that board, push in the key for that circuit of the conductor and tap the board gently. The textbook diagram shows that the iron filings line up in concentric circles around the conductor. While it should be correct to show field lines in that manner since we're considering an individual field line, it shouldn't be that way for iron filings. If a cross section of this concentric pattern is analyzed for the field, it will turn out to be a wave-form rather than a curve. Since the field B is supposed to be directly proportional to the current and inversely proportional to the distance from the conductor, the latter should prevail. I cannot make a sane justification for the concentric pattern of circles.

2. Sep 23, 2010

### Ralph Spencer

Moreover, to map a field line, we use a compass needle. Since the needle is AT THAT POINT is why it shows that direction. If it were to be placed, say at one nanometer from that point the field would be in the same direction. Only thing that would drop a bit is the intensity, which is reducing due to distance from the conductor. For no reason should the iron filings prefer the position on the IMAGINARY field line rather than their initial position.

3. Sep 23, 2010

### granpa

Last edited: Sep 23, 2010
4. Sep 24, 2010

### Ralph Spencer

Negative, sir! That's the point of my question. You're considering only one line. If you check the "theoretically next" line (which is just one theoretical point, infinitely small distance) away from the initial line, the direction will be same. If you plot this, with the darkness of the line proportional to the field, what you should get is a gradient decrease in the darkness, which seems more compatible with the formula rather than a waveform decrease, which decreases in amplitude with time.

Basically, why do they want to pull into the field line? Their current position also rests on a field line.

Last edited: Sep 24, 2010
5. Sep 24, 2010

### granpa

"they have a natural tendency to pull one another into long lines"
Why?
Because:
iron filings pull magnetic field lines into themselves
why?
because:
http://en.wikipedia.org/wiki/Magnetic_permeability

The rest of your post is indecipherable

Last edited: Sep 24, 2010
6. Sep 24, 2010

### Ralph Spencer

I understand permeability as the property of substances that describes their ability to allow formation of magnet fields in and around them.

Lets clear up things from the basics: If I were to lay perfectly uniform iron filings(uniform in everything: size, mass, composition) in unit area, with their quantity proportional to the field there, and then tap the board, would I encounter the lines?

If I were to make a very large current flow through the conductor, all the filings would just stick to it, correct?

Last edited: Sep 24, 2010
7. Sep 24, 2010

### granpa

'Allow' is perhaps not quite the right word to describe it.
In the presence of an externally applied magnetic field the iron itself becomes magnetized
and its own magnetic field adds to the already existing external field.
That is why the field lines seem to be pulled into the iron filings.

Since the iron filings are themselves little magnets and magnets tend to align north to south
(you can see this easily yourself with any 2 permanent magnets),
the iron filings tend to form lines.

http://en.wikipedia.org/wiki/Magnetization

what grade you are in and how much physics you have studied.

From your profile page I see that you are a high school graduate
and from your other posts I see that you have a good grasp of many complex subjects.
I am a little surprised that you are having so much trouble with this.

Last edited: Sep 24, 2010
8. Sep 24, 2010

### Ralph Spencer

Thanks for quick answer. That quite answers the question. I would still certainly appreciate an answer to my first question in the last post about the uniform filings.

I don't have much mathematical background in the subject; the main drawback. I just gave it a thought after you talked about permeability, and got the picture in no time. Decided to post that I got the idea, only to see that you've answered. :)

9. Sep 25, 2010

### mishrashubham

I have this doubt too! I just cannot comprehend this abstract concept of imaginary magnetic field lines. It is as if the experiment is made to just to put this idea into the children's minds that fields are made of lines.

10. Sep 25, 2010

### granpa

Field lines is just a mental trick to visualize an inverse square law in 3 dimensions.
(or an inverse first law in 2 dimensions)

When you go to higher dimensions the magnetic field is no longer a vector field but is a tensor field.

11. Sep 25, 2010

### mishrashubham

Ok may be this is getting above my knowledge levels (I've no idea what tensor is).

However for the mental trick that you said, what do we mean by the "direction" of these magnetic field lines then? Aren't they supposed to make it easy for us to understand?

12. Sep 25, 2010

### granpa

Tensors are made of vectors just like vectors are made of scalars (numbers).
Figuring out tensors is probably going to be my next big project.

Field lines are important.
You need to understand how they work.

The lines end at charges and have tension along their length.
(thats why opposite charges attract).
The number of lines is proportional to the number of charges.
The lines repel one another and therefore spread out as much as possible.

Magnetic field lines never end.
They just go around in circles.

The divergence of the electric vector field is nonzero only where there is charge.
the curl of the magnetic vector field is nonzero only where there is current.

Your profile page says "Interested in physics but always fall behind because I don't know calculus".
I learned calculus and field lines at the same time from a very good 'calculus for electrostatics' textbook.
It was fascinating and very intuitive.
I couldnt put it down.
I highly recommend it.

You need to understand calulus.
You can easily learn elementary calculus in a day.
Derivatives are easy.
elementary integrals are easy.
complex integrals are hard but can be done by computers.
There are some online calculators that will do them for you.

Last edited: Sep 25, 2010
13. Sep 25, 2010

### mishrashubham

Thanks for the reply but I couldn't get most of what you said. Sheesh I really need to study about this in depth. And also thanks for the recommendation, I'll try searching for that book. Could you please mention the name of the author if you remember.

Every time I try to delve into some advanced science I understand the physics bit but am overwhelmed by the math involved. Hence I never get the complete picture because. I need to have knowledge of that complicated equation before progressing. I'm sure after learning calculus I will be able to learn some things that I've been trying to understand for a long time.

Last edited: Sep 25, 2010
14. Sep 25, 2010

### granpa

Its not as complicated as you probably think it is.
If I knew what part you didnt get I could probably explain it to you.

15. Sep 25, 2010

### mishrashubham

I couldn't understand what you meant by tension along the lines.

16. Sep 25, 2010

### mishrashubham

Thanks for all your replies. I really appreciate your willingness to explain me all these but I must retire for the night (I don't know what the time is over there but here in India its almost midnight and my mother is not letting sit in front of the laptop anymore). Only if you could just name the author of the textbook that you mentioned I would be really glad.

Thank You again

17. Sep 25, 2010

### granpa

Think of them as stretched rubber bands. They want to shrink. Thats tension.

I no longer have the book. It was an old book.

18. Nov 28, 2010

### mrollin

I believe I share the question with the original asker; let me try a different explanation of the question.

Field lines are only a schematic drawing on paper, like contour lines on a topographical map, that help us visualize where the field is and how it is shaped. There is no physical correlate of the lines per se, just a continuous field that follows the contours partially described by the lines.

However, iron filings coalesce in a magnetic field, in real life, into lines that appear shockingly like the field lines in our diagrams. So the questions are:

1. Why do they arrange themselves so nicely into lines, instead into a uniform sheet or volume (albeit all parallel to one another in their longest dimension), and
2. Why are the lines arranged so regularly?

19. Nov 28, 2010

### Jack the Stri

I think the layman's answer, paraphrased from the answers above, is basically that because the iron filings are magnetised, they attract one another and just end up as one long coalesced line. This is a secondary effect of the presence of a field, as the primary effect is the magnetisation of the filings and their alignment with the field, which then causes them to attract each other, as magnets do.

At least that's my take on it, correct me if I'm wrong.

20. Nov 28, 2010

### mrollin

I think that's a great answer for #1. But it doesn't account for #2; why are these lines so evenly spaced?

Although, I just did a Google image search for iron filings, and I'm finding that perhaps the lines are not as evenly spaced as I've asserted.