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During a recent stay I showed my granddaughter (8) how to display magnetic lines of force with iron filings.

She asked me a question I couldn't really answer so I will ask the combined wisdom (mainly because I can't find an answer on the internet in general)

Her question:
The iron filings line up along the lines of magnetic force - Why are there gaps between the lines?

My initial response is that the iron filings become magnetic and so repel each other so they form up in the lines we see because they are quite big but the magnetic lines of force are either much closer together or one continuous "beam"

Any insight?

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As others have said, you gave the exactly the right answer. The magnetic field is continuous -- it has a value everywhere in space. The iron filings become aligned by the field wherever they are, but also then have their own magnetization (much smaller than that of the source magnet, of course). Thus, they influence (repel) their side-by-side neighbors, while attracting their front-and-back neighbors. This leads to the visible "lines" separated by gaps.

The little filings are all miniature magnets and repel each other .

ie like poles repel.

If you use a film which aligns with flux direction it does not  make individual lines.
see my ible on the right. ------------------------------------------------------------------------------->>
second red down.

A

They do not repel each other following a flux line because they align N-S-N-S-N-S- - - -N-S...

One other characteristic of magnetic flux lines..
• They actually deform and
• Prefer to squeeze into more permeable material like IRON filings.
• This flux squeeze into metal has a flux density LIMIT called Saturation.
• After a filing is saturated, the excess flux travels through the  surrounding air.
• This property increases the apparent separation  and
• The iron filings line up along the lines of magnetic force.

So the magnetic field is a continuous force? in the same way Gravity is a continuous force everywhere.

Thanks guys - seems my explanation was right - I like to encourage the young scientist whilst they are still interested.

The amount of filings influences the lines as much as they push apart.

If you used enough filings you would have a puffy spikey ball of iron.

Joe