File:Helmholtz coil, B magnitude cross section.svg
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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
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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. |
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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()
File history
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| Date/Time | Thumbnail | Dimensions | User | Comment | |
|---|---|---|---|---|---|
| current | 00:09, 13 May 2014 | | 540 × 540 (250 KB) | Morn | {{Information |Description ={{en|1=Cross section of B magnitude in a Helmholtz coil (actually consisting of two coils, one at the top, one at the bottom in the plot). Field strength is scaled by center value, isolines are at .5,.8,.9,.95,.99,1.01,1.... |
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