# Magnetic field through ferrous material and across air gap

1. Jun 10, 2010

### Stugotz99

I am attempting to determine how strong a magnetic field will be on the other side of a thick material and then across an air gap.

For instance, I have a closed steel cylinder with a steel piston inside it. I plan to affix a permanent magnet to one side of the piston (inside the cylinder). I am looking to use another cylindrical magnet that can slide inside a separate stainless steel cylinder mounted outside and parallel to the first. My goal is to gage the position of the steel piston within the steel cylinder by viewing the position of the second magnet through windows in the SS cylinder. It will be necessary to have a small air gap between the two cylinders for mounting purposes. Hopefully this description makes sense. A hall effect sensor would work great to determine the magnet's position but I need a mechanical analogue thus not requiring any electric signal. Precision is not terribly critical, with relative position being more important.

So, I am attempting to calculate the required strength/size/material of the two magnets based on the thickness of the first steel cylinder and the air gap between the two cylinders.

Thanks!!

2. Jun 10, 2010

### Bob S

The magnetic field B (Tesla) is continuous (because div B = 0) across boundaries. If it is perpendicular to a surface, the normal component is the same on both sides. Stainless steels are either magnetic (martensitic, 400 series) or non magnetic (austenitic, 300 series).

Bob S

3. Jun 15, 2010

### Stugotz99

Well, after doing some more research, and ordering some expensive magnets, my research seems to disagree with what is being said.

Do materials not have different degrees of magnetic permeability? Remember, in my case the magnetic field must first pass through a carbon-steel cylinder.

Quick checks with a guass meter show that the magnetic field is being redistributed through the steel cylinder and is no longer as strong as it would be in free space...

This may not work after all...

4. Jun 15, 2010

### LostConjugate

div B = 0 in vacuum right?

The Relative Permeability of steel μ/μ0 = 100

I guess that means steel permits more than vacuum, which should give you a stronger field.

Last edited: Jun 15, 2010
5. Jun 17, 2010

### Antiphon

Only the normal component is continuous. The tangential components of B are discontinous for a material interface of two different permeabilities.

As a practical matter, a steel pipe will prevent your sensor from making an accurate position measurement. Switch to PVC and you will be in fine shape.