# Magnetic Force that Makes a Solenoid Valve Work

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1. Aug 14, 2016

### AvroArrow

Hi guys,
I am having quite the struggle finding a good resource to explain the difference between the magnetic force associated with moving charged particles (Lorentz Force) and just the regular force exerted by a magnetic field on a magnet or ferromagnetic material. I am trying to apply this to the solenoid valve, which is essentially just an electromagnet that creates a magnetic field which moves a plunger.

In this video:

the gentleman says at around the 0:08 mark that the magnetic field pulls the plunger, I am curious as to what force is pulling this plunger. It is not the Lorentz force because there are no charged particles moving in the plunger, so what other type of magnetic force is at play here?

Any sort of clarification or resources would be very appreciated,
Thanks.

2. Aug 14, 2016

### Hesch

A magnetic field concists of two different fields:

- A magnetic field strength ( H-field ) with unit: A/m
- A magnetic induction ( B-field ) with unit: Tesla

. . just like electricity consists of voltage and current.

The magnetic energy density in a field = ½ * B * H [ J/m3 ]
At the end of the rod, connected to the valve, the B-field will be the same at each side of the surface, but the H-field will not because the permeabilty in air/iron is different:

In air: B = μ0*H
In iron: B = μ0r*H

So if μr as for iron = 900 ( typical value ), the H-field will become 900 times stronger in air than in iron, and so will will the magnetic energy density.

Now, mother nature hates high magnetic energy density, and wants somehow to get rid of it. So if that high density in a volume of air just outside the rod could be substituted by iron, mother nature will be happy, and will pull iron into the volume of air.

The pulling force can be calculated from:

F = -dE/ds , E = total magnetic energy in the system, s = length that the rod is moved.

3. Aug 14, 2016

### Jony130

4. Aug 14, 2016

### AvroArrow

Thanks, awesome link,really cleared things up for me. I am always amazed by the incredible "google search game" you guys have. I have no idea how you guys find these helpful links while all I can find is complicated PhD thesis papers that are always way beyond me. Is there another secret internet I am not aware of? ha ha thanks again.

Cheers,

5. Aug 14, 2016

### AvroArrow

Thanks, I think I am slowly figuring it out. I never put the pieces of magnetic flux and magnetic field strength together until now. This pull force of the magnet seems to completely independent of this Lorentz Force I have studied in school. My understanding of this pull force is it is the result of the gradient between magnetic energy density which results from the difference in permeability of the air and the ferromagnetic material. The flux lines don't care about the difference in permeability, (is that why the B field is the same on each side of the surface? ) but the magnetic field strength does care about the permeability difference which is why there is a gradient, which is why the force is generated.

Cheers,