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I'm having a hard time trying to understand a very basic electromagnetism related question, related to how a solenoid valve works. Consider the image below:

enter image description here

Why is there a force exerted on a ferromagnetic material (at rest, i.e. zero initial velocity) concentric with a solenoid fed with DC current?

I would say that besides the on/off moments, where there is a variation of the magnetic field, the field will be constant and therefore no force would exist.

What am I missing here?

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I think you are missing the fact that the field of the solenoid (which is relatively uniform inside the coil) will magnetize the core and create magnetic poles in it (see this). The interaction of the field of the coil with the field of the core will pull the plunger into the coil.

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  • $\begingroup$ It must be pretty obvious, but I don't understand what interaction is that. Essentially, why will two magnets attract if the magnetic field is constant? $\endgroup$ – cinico Nov 22 '16 at 17:13
  • $\begingroup$ The field outside the coil is not uniform. If you look at the picture, the density of the H-lines outside the coil changes, which means that there is a gradient. If you imagine a very long coil, say 1 meter, and a 10 cm rod, it will move inside until the field becomes relatively constant. And the reason why two magnets interact is still the Lorentz force. You can roughly understand a magnet as a set of microscopic current loops. The electrons cirling within them will be affected by the external magnetic field via the Lorentz force. $\endgroup$ – Ilya Nov 22 '16 at 19:25
  • $\begingroup$ But my problem understanding this is that Lorentz force describes a system where I know the electrical current (q.v), but I can't relate this with the magnetic strength of a magnet. $\endgroup$ – cinico Nov 22 '16 at 19:40
  • $\begingroup$ There is a direct relation: en.wikipedia.org/wiki/Magnetic_moment. $\endgroup$ – Ilya Nov 22 '16 at 20:06
  • $\begingroup$ For the simpliest case of a charge q circling around an orbit of radius r, the magnetic moment is: (1/2)q[rv], for a magnet you would have a set of such loopls and the total magnetization would be an integration over the volume containing all of them: en.wikipedia.org/wiki/Orbital_magnetization $\endgroup$ – Ilya Nov 22 '16 at 20:12

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