File:Helmholtz coil, B magnitude cross section.svg
Summary
| Description |
English: Cross section of B (magnetic field strength) magnitude in a Helmholtz coil (actually consisting of two coils: one at the top, one at the bottom in the plot). The eight contours are for field magnitudes of 0.5 B0, 0.8 B0, 0.9 B0, 0.95 B0, 0.99 B0, 1.01 B0, 1.05 B0, and 1.1 B0, where B0 is field strength at center. The large center area has almost uniform field strength. |
| Date | |
| Source | Own work |
| Author | Morn |
Licensing
I, the copyright holder of this work, hereby publish it under the following licenses:
This file is licensed under the Creative Commons Attribution-Share Alike 3.0 Unported license.
- You are free:
- to share – to copy, distribute and transmit the work
- to remix – to adapt the work
- Under the following conditions:
- attribution – You must give appropriate credit, provide a link to the license, and indicate if changes were made. You may do so in any reasonable manner, but not in any way that suggests the licensor endorses you or your use.
- share alike – If you remix, transform, or build upon the material, you must distribute your contributions under the same or compatible license as the original.
 |
Permission is granted to copy, distribute and/or modify this document under the terms of the GNU Free Documentation License, Version 1.2 or any later version published by the Free Software Foundation; with no Invariant Sections, no Front-Cover Texts, and no Back-Cover Texts. A copy of the license is included in the section entitled GNU Free Documentation License. |
You may select the license of your choice.
Python source code
from pylab import * # needs Matplotlib
r = 1
res = 500 # grid resolution (100 seems to be sufficient here and will create a smaller SVG file)
figure(figsize=(6, 6))
axes((0,0,1,1), frameon = False)
def dist3(a,b,c,d,e,f):
return maximum(r, sqrt((a-d)**2 + (b-e)**2 + (c-f)**2))
x = linspace(-150, 150, res)
y = linspace(-150, 150, res)
X,Y = meshgrid(x,y)
F = zeros((res,res,3))
# loop over two coils
for coils in 1,-1:
# sum field contributions from coil in 10-degree steps
for p in range(0, 360, 10):
xc,yc,zc = (100*sin(pi*p/180),50*coils,100*cos(pi*p/180))
MAG = 1/((r+dist3(X,Y,0,xc,yc,zc))**3)
# (We leave out the necessary constants that would be required
# to get proper units because only scaling behavior will be shown
# in the plot. This is also why a sum instead of an integral
# can be used.)
Z = cross((X[:,:,newaxis]-xc,Y[:,:,newaxis]-yc,-zc),(-zc,0,xc))
F += Z[0,:,:]*MAG[:,:,newaxis]
B = sqrt(F[:,:,0]**2+F[:,:,1]**2+F[:,:,2]**2)
# scale field strength by value at center:
B = B / B[res/2,res/2]
contour(x,y,B, levels = (.5,.8,.9,.95,.99,1.01,1.05,1.1))
# add wire symbols:
scatter((100,100,-100,-100), (50,-50,50,-50), s = 400, color = "black")
axis((-130, 130, -130, 130))
xticks([])
yticks([])
savefig("Helmholtz_coil,_B_magnitude_cross_section.svg")
show()