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# Electrical Engineering/Converting the field strength of an electromagnet into newtons

Question

Three quarter turn coi
Hello Cleggsan,

How are you? I hope you are doing well. Thanks for your previous answer and thanks for the patience!

I think I have made a big mistake, but I can't work out how I did it. I am having trouble with some calculations I have been trying to do to determine the strength of an electromagnet in Newtons/gram force.
I have found a formula for this calculation, but the results I get do not seem right, and I am wondering if you can see where I am going wrong.

The formula I have been using is
"a magnetic field with density of 1 Tesla generates one newton of force per ampere of current per meter of conductor."
(My electromagnet has a 3/4 turn coil, 0.04mm in diameter and 0.023mm in length, so I guess the first question I should be asking is whether the above formula actually applies in this case, or whether it needs to be altered in some way.)

My magnet has -
a field of 0.0000398 tesla
0.0000942 meters of current conductor = 0.75 turn x (.00004 meters x 3.14)
current of 0.00000486 amps

So I calculated
tesla x amps x meter of conductor = newtons
0.0000398 tesla x 0.00000486 amps x 0.0000942 meters of current conductor =
1.82e-14 newtons = 0.0000000000000182 newtons = 1.85e-12 gram force

I think I must be doing something wrong, because even though my electromagnet is admittedly very small, the results for Newtons that I end up with still seem very low.

Just to play around with the numbers, I also did some calculations using a value of 1 telsa and 1 amp, and I still got a Newton value that seems very low.
1 tesla x 1 amp x 0.0000942 meters of current conductor = 0.0000942 newtons = 0.009605727 gram force

Am I doing something wrong? My understanding is that a 1 Telsa magnet is very strong. I read on wikipedia that a 1.25 tesla "coin-sized neodymium magnet can lift more than 9 kg, can pinch skin and erase credit cards."  A refrigerator magnet has a field of 0.005 tesla, and I am thinking this must weigh more than 0.000045 grams.
With these in mind, 0.0000942 Netwons = 0.009605727 gram force seems like such a low value for the force of the electromagnet in my calculation. Am I right in thinking this? Should the force value of my electromagnet be higher?

Thanks as always, domo arigato
Eddie

Konichiwa or maybe Ohaiyogozaimas in your time.....

I did not go through your calculations but they don't seem too far off.  The problem is the length of your coil wire is so very short that the current can't get enough force going.

Practically, if you look at physical solenoids they almost always have a coil around the push rod form of many, many turns.  Maybe a hundred or two hundred turns in order to get enough magnetic strength built up to push out the metal rod.

Whilst the web page below does not relate to your project directly, the principles remain the same.  You can see by this example that in order to get enough magnetic force to operate the actuator that lots of turns are needed to build up the magnetic field:

http://en.wikipedia.org/wiki/Solenoid

Domo

Electrical Engineering

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#### cleggsan

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