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Name: Aaron L.
Status: educator
Age: 20's
Location: N/A 
Country: N/A
Date: 10/15/2004


Question:
My father had a question about magnetic force that I cannot find the answer to. He and a friend were trying use a very thin piece of steel to hold up a light that was designed to stick to metal surfaces via a built-in magnet. The light worked fine on a metal cabinet, but could not support itself on the thin piece of steel. At what point does the thickness of a metal begin to affect its attractive force to a magnet? And now that I am curious about it, can anyone recommend a good source that I might be able to look up to study these effects?


Replies:
I will assume your magnet is a relatively strong one, and the light is a heavy thing, and your thin steel is a good magnetic alloy. (Virtually all galvanized steel sheet is "good", in this sense.)

Then the very thin steel can only carry a fraction of the magnetic field lines that the strong magnet tries to push through it. Every passively magnetic material like steel has a conduction limit, called the "saturation flux density". For steel or iron it is about 20,000 Gauss. It conducts the 20,000 easily, but any more than that feels like it is pushing through empty space (air). The strongest rare-earth magnets, within themselves or across short air gaps, make a flux density of only 5,000 gauss. Other strong magnets tend to be about 3000 Gauss.

The "holding force" arises from the stretching of the portion of the magnetic path which has to go through (poorly permeable) air, instead of easily permeable iron. In addition, long distances through air tends to reduce the net flux which tries to reach outside the magnet. This explains why the magnet's attractive force is greatest when the magnet is almost touching the steel.

For a 3000-gauss magnet to reach it's best holding force, all the flux lines need to be conducted around the loop, so the thickness of the steel will need to be roughly 3000/20000 or 15% of the width of each N-pole or S-pole spot on the face of the magnet. Thinner steel will feel attraction only in proportion to it's thickness.

..............................................................
.Magnet holding to steel sheet makes closed loops 
.  of magnetic flux lines:
.  +----------------------+    Magnet w. N and S pole-spots  
.  |    ==<==    ==>==    |    on the bottom face.
.  |  //     \\//     \\  |   ( magnetic flux lines: //||\\=>= )
.  | NN       SS       NN |
.  +/||\-----/||\-----/||\+    < - air gap between magnet face 
.-----\\\---//--\\---///-----------------     and steel face
.       ==>=      ==<=       steel sheet
.----------------------------------------
..............................................................

You can feel out the locations of these pole-spots which the tip of a nail or a paper-clip is drawn towards:
..............................................................
.Feeling out the pole-spots of the magnet:
.  +----------------------+
.  |    ==<==    ==>==    |    Magnet w.
.  |  //     \\//     \\  |    N & S pole-spots
.  | NN       SS       NN |    on the bottom face.
.  +/||\-----/||\-----/||\+
.   / |  \_/ /|  \ _ / | \
.   |  \     M        /   |         M: nail or paper-clip
.   |    \ _ M _ _ <-/   /
.    \       M         /
.      \_ _ _M _ _ _ /  flux lines in air, and 
.            M                conducting through the nail
..............................................................


Many of these surface-holding magnets use a block of simple ceramic magnet with a thick sheet of shiny galvanized steel collecting magnetic lines and conducting them over to the surface to be held. (see ASCII sketch below) It is a fair bet that your steel surface never needs to be thicker than these pole-piece slabs. On the other hand, your metal should be at least 1/3 as thick, and you can notice the loss of strength even at half as thick. Suppose the pole-piece was 1/8 inch thick. That is 125 mils or 0.125 inch. Then steel flashing 10-mil (0.010 inch) thick would achieve only 8% of the best holding force of the magnet. I imagine the manufacturer gave you only enough magnet to hold up the light with 50% of its best force. Even the 20-mil structural strapping common in hardware stores might not be enough.
..............................................................
.Simplest Magnet with one (top-to-bottom) polarization
.  and U-shaped steel pole piece:
.    _______________________________
.   /  ___________________________  \ - steel pole piece
.   | |   +-------------------+   | |
.   | |   | N ^ N ^ N ^ N ^ N |   | |                
.   | |   | | | | | | | | | | |   | |
.   | |   | S ^ S ^ S ^ S ^ S |   | |   ( magnetic flux 
.   |_|   +-------------------+   |_|     lines: //||\\=>=/-  )
.--/|||\---/-|-|-|-|-|-|-|-|-\---/|||\-----------------
.    \\==>==/-/- /   \ - \ -\==<==//     steel sheet
.------------------------------------------------------
..............................................................

You may find some hobby motors to which nails can adhere magnetically. This is the same kind of issue as your question. The thickness of steel in the outer shell is insufficient to conduct all the flux lines of the magnets inside. These motors can actually be made a little better by wrapping another layer of steel around them. Meanwhile, you can put that light's magnet up against the thin steel and feel out how much of the magnetic field reaches into the air behind the steel sheet. This is a measure of the holding force you've lost.

nice question-

Jim Swenson

PS- all my percentages above are fuzzy. They may be a factor of two away from the real values, but they express the sense of the situation. I think somebody invented algebra for things like that, long ago...)



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