I am working on a electromagnet project to collect metal shavings off the floor after machining.

I have a formula for the magnetic strength at a distance from the ends, but not parallel to the coil. How do I calculate F parallel to the coil?

The formula I have now is: $$F = \dfrac{(NI)^2 μ_0 A}{2 g^2}$$

[ Edit - formula from http://depts.washington.edu/mictech/optics/sensors/week2.pdf ]

Here is a visual example of what I am looking for: Field strength

  • \$\begingroup\$ Your image link appears to be broken. If you clock on the "add image" button in the qjestion editor, you can upload & insert the image directly into your post. \$\endgroup\$ Feb 1, 2016 at 16:24
  • \$\begingroup\$ You would do better to bend your electromagnet core into a U or otherwise construct a core that allows both ends to point at the floor for more effective pickup. If you are trying for a wide path, many magnets. This type of device (magnetic sweeper) is also implemented commercially with many rare earth magnets...no pesky power cord. \$\endgroup\$
    – Ecnerwal
    Feb 2, 2016 at 0:31

1 Answer 1


How do I calculate F parallel to the coil?

It doesn't have to be an electromagnet to show that the force halfway along is zero: -

enter image description here

Note the iron filings at the centre of the bar magnet are not attracted to the centre - they form lines (with other iron filings) that attempt to bridge the ends of the bar magnet.

  • \$\begingroup\$ good point. Never thought off it that way. \$\endgroup\$ Feb 1, 2016 at 20:08

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