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I am trying to calculate the magnetic field (in tesla/gauss) of an electromagnet that is very small and has very few windings. For example 12 windings over 0.003 meters. I know this is not going to produce a very strong field, but I would like to pulse a strong current through the coil very briefly to make it stronger. I have found an number of sources listing the formula for the calculation of magnetic field strength -

$$B = permeability * \rho * I= (μ * μ0)*(number of turns/core length)*I$$

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

My question is

  • can this formula be applied to my electromagnet design?

  • Does the size and low number of windings on my electromagnet mean this formula is not valid?

  • Is there any other way I can calculate/estimate magnetic field?

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    $\begingroup$ Why would you think the formula would not work? $\endgroup$ – Jiminion Mar 6 '15 at 17:18
  • $\begingroup$ Another person told me it was not valid for small electromagnets after I compared the results I got from that formula, and one for a U shaped electromagnet that I found on en.wikipedia.org/wiki/Electromagnet which was turns*current = B((Lcore/μ)+(Lgap/μ0)) The problem was, I got a smaller result in Teslas for the U shaped electromagnet than the straight core electromagnet. I know something is wrong with this, but I am not sure what. $\endgroup$ – EddieP Mar 6 '15 at 17:42
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    $\begingroup$ The field depends on the shape. You can't apply the formula for a straight magnet and expect it to give the right result for a U shaped magnet, or vice versa! $\endgroup$ – Floris Mar 6 '15 at 18:10
  • $\begingroup$ The formula I was using for the U shaped magnet was taken from en.wikipedia.org/wiki/… Where it said "For an electromagnet with a single magnetic circuit, of which length Lcore of the magnetic field path is in the core material and length Lgap is in air gaps" the formula is turns*current = B((Lcore/μ)+(Lgap/μ0)) I am not sure if this is the correct formula for a U shaped electromagnet or not. Does anyone know the formula for the U shaped magnet? Am I using the wrong one here? $\endgroup$ – EddieP Mar 6 '15 at 18:22
  • $\begingroup$ For a pulse, there is also the problem of self-induction, which may limit the maximal current. $\endgroup$ – Pieter Dec 24 '17 at 19:46
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To find the strength in gauss you must multiply the number of turns of wire in the electromagnet by the amperage.So for a example if you have a electromagnet with 20 turns of wire with 10 amps going through the wire then you multiply 20 by 10 and that will equals 200 so the magnetic feild it's producing is 200 gauss.Hopes this helps:)

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what's the shape of the magnet pole?

For a normal multipole magnet, the field for a $2n$ multipole is given by: $$B_y+iB_x=n\frac{\mu_0NI}{r_0}(\frac{x+iy}{r_0})^{n-1}$$ where $r_0$ means the distance between the pole and the origin of the coordinate system. $NI$ means each pole consists of $N$ turns of wire carrying current $I$.

So, $n=1$ is a dipole with gap $2r_0$; and $n=2$ is a quadrupole with field gradient $\frac{\partial B_y}{\partial x}=\frac{\partial B_x}{\partial y}=\frac{2\mu_0NI}{r_0^2}$

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