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originally posted by: Dr X
a reply to: DeadCat
When you spread iron filings near a magnet, there are distinct lines that they surround and align with. If it was simply a field then the filings would spread uniformly. Physics textbooks conveniently ignore this fact.
You're right that there vector fields instead of lines in the physics, but the iron filings do form distinct lines and you didn't really explain why. It's because if there aren't many filings, they form N-S magnets themselves and then they tend to form a "chain" of NS magnets attracting each other, and these chains of NS magnets are what form the lines.
originally posted by: mbkennel
This isn't true. The "lines" are human-friendly visual representation of a vector field, the same way that contour lines on an topographic elevation map are a human-friendly representation of an altitude scalar value on an otherwise 2-d map.
There are no lines in the physics, just vector fields.