Dear Colleagues
In the literature, I have found the following formula for the magnetic field in the centre on the solenoid with finite length on its axis:
Bz(0) = 0.5*mi0*N/L*I/(r2-r1)*(a*log((sqrt((a)^2+r2^2)+r2)/(sqrt(a^2+r1^2)+r1)) - b*log((sqrt(b^2+r2^2)+r2)/(sqrt(b^2+r1^2)+r1)))
where
L = a +b - length of the solenoid (commonly a=b=L/2)
r1 - inner radius of the solenoid
r2 - outer radius of the solenoid
N - number of solenoid turns
I - current passing through the solenoid
Do You maybe know what is the full formula for the magnetic field on the solenoid axis Bz(z) and where I could find its derivation for such formula?
I will be grateful for your help!
Best Wishes,
Piotr
Take a look on:
- Introduction to Magnetism and Magnetic Materials, Third Edition, By David Jiles, which can be found on-line. There are solutions for different simplifications (thin/thick, finite/infinite).
- Or, for polish readers, subsection 5.5.6. at "Podstawy elektromagnetyzmu" by Henryk Rawa.
Pytanie o pole magnetyczne dotarło też do mnie, ale ja się na tym kompletnie nie znam. Pozdr. B. Mochnacki
magnetic field inside solenoid can be calculated as
H=k* current =n/l * current
where n is number of turns and l is length of solenoid
Take a look on:
- Introduction to Magnetism and Magnetic Materials, Third Edition, By David Jiles, which can be found on-line. There are solutions for different simplifications (thin/thick, finite/infinite).
- Or, for polish readers, subsection 5.5.6. at "Podstawy elektromagnetyzmu" by Henryk Rawa.
Hi. I guess the best reference is Durand, Magnetostatique. It is a French book, and I never heard about English translation, but it is worth the effort!
To get the correct formula you should start from Biot-Savart law (see: https://en.wikipedia.org/wiki/Biot%E2%80%93Savart_law ) rather than from Ampere's law. Some approximations will be unavoidable, too: current density not depending on location in the wire, each single coil turn approximated by torus, neglecting the other current-carrying conductors (those powering the coil), etc. As far as I remember, even after such simplifications, it is possible to get closed form expression describing the field along the symmetry axis (only). The fields at other locations are expressed by elliptic integrals, unfortunately.
Any good UG textbook will show you how to calculate the axial field close to the axis via integration of Biot Savart. Best " modern " one I know is Wangness : IElectromagnetic fields ISBN0-471-04103-3.
But the complete field distribution on and off axis has to be done numerically .(but there are some handy " analytic" approximations) It has to take into account the pitch of the winding . Designers of MRI machines probably know as much as anybody( leaving aside CERN engineers/ designers) . Look there for more detail than you probably want .
For interested in this topic I suggest to read this paper:
P. Gas, and E. Kurgan, “Cooling effects inside water-cooled inductors for Magnetic Fluid Hyperthermia”, 2017 Progress in Applied Electrical Engineering (PAEE), IEEE Xplore, 2017, art. no. 8008997, [pp. 1-4].
Available at: http://dx.doi.org/10.1109/PAEE.2017.8008997
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