I am looking for the B-field of a real coil.

[0xDEADBEEF]

I am looking for the B-field of a real coil. So a straight piece of pipe with some current density. Is it correct that there is no analytical solution to this?

It would be enough if I had the field of a current rotating in a cylinder obviously. I am working on some Biot-Savart but either I get some ugly double roots or roots mixed with trig functions in my integrals.

Does anyone know more? I do need the off center field as well!

 

[ozymandias]

I can't help you with the off-center field, but there is a closed form solution for the on-axis field. It's axial (for obvious symmetry reasons) and equal to (in SI units):

$B_z(z) = \frac{\mu_0 n I}{2} \left( \cos(\alpha_1) - \cos(\alpha_2)\right)$

where alpha_1, alpha_2 are the angles measured at z between the coil's axis of symmetry and the coil's upper and lower rims (assuming current starts at the bottom and circulates its way to top). n is the number of turns per unit length.


-----
Assaf
http://www.physicallyincorrect.com"

 

[Bob S]

Ozymandias' answer is a nice form of the Biot Savart equation appropriate for solenoids. It is important to note that for a long solenoid, B is independent of coil diameter. It is also useful to put some numbers in for a typical coil (μ₀ = 4 pi x 10^-7 Henrys per meter). using n=1000 turns carrying 10 amps, the magnetic field is 0.0126 Tesla (126 Gauss). Compare to the Earth's field (~ 1 Gauss) and the field of a neodymium-iron-boron permanent magnet (~ 1 Tesla = 10,000 Gauss).

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