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Question
Hello Mr Nelson,

I am having a problem calculating the field strength of an electromagnet and I was wondering if you could give me some guidance.

The formula I have used for calculating the magnetic field, in telsa is

permeability x turn density x current = magnetic field

The (hypothetical) electromagnet I want to measure is 0.000023 meters long with 0.75 turns, giving it a turn density of 32,608.69565.

The current is 0.00486 milliamps
I have read that the relative permeability of magnetic iron is 200.

So, I did the following calculation
permeability x turn density x current = magnetic field
200 x 32,608.69565 x 0.00000486 amps = 31.69 tesla

Does this seem right to you? It seems like quite a high value of tesla.

I have also used some online calculators to check my calculations but I have got some different results from each.
This one gives me the same results as my calculations; 31.6957 tesla

http://www.calctool.org/CALC/phys/electromagnetism/solenoid

but this one gives me the field strength as 0.0000398 tesla

http://hyperphysics.phy-astr.gsu.edu/hbase/magnetic/solenoid.html

Have I done something wrong? Are my calculations correct?

Your help would be much appreciated.

Thank you and best regards,
Eddie

Answer
Well, that's a ridiculous magnet, but you forgot something really important aside from its ridiculous dimensions.  A solenoid is long and thin with many turns, so that it's really long compared to its width.  You have a 3/4 turn magnet that's reeeeally tiny.  Not a solenoid.  End effects make Ampere's law inapplicable to use as an approximation.  You used the relative permeability.  You forgot the factor of 4*pi*10^-7 (permeability of empty space), which really brings the number down.  :)  You have to multiply the relative permeability by the permeability of empty space, makes your answer agree with the calculator.  It's the little things...

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Dr. Stephen O. Nelson

Expertise

I can answer most basic physics questions, physics questions about science fiction and everyday observations of physics, etc. I'm also usually good for science fair advice (I'm the regional science fair director). I do not answer homework problems. I will occasionally point out where a homework solution went wrong, though. I'm usually good at explaining odd observations that seem counterintuitive, energy science, nuclear physics, nuclear astrophysics, and alternative theories of physics are my specialties.

Experience

I was a physics professor at the University of Texas of the Permian Basin, research in nuclear technology and nuclear astrophysics. My travelling science show saw over 20,000 students of all ages. I taught physics, nuclear chemistry, radiation safety, vacuum technology, and answer tons of questions as I tour schools encouraging students to consider careers in science. I moved on to a non-academic job with more research just recently.

Education/Credentials
Ph. D. from Duke University in physics, research in nuclear astrophysics reactions, gamma-ray astronomy technology, and advanced nuclear reactors.

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