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

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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()

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13 May 2014

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Date/TimeThumbnailDimensionsUserComment
current00:09, 13 May 2014Thumbnail for version as of 00:09, 13 May 2014540 × 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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