File:VFPt capacitor-infinite-plate uniform.svg
![File:VFPt capacitor-infinite-plate uniform.svg](https://upload.wikimedia.org/wikipedia/commons/thumb/5/57/VFPt_capacitor-infinite-plate_uniform.svg/800px-VFPt_capacitor-infinite-plate_uniform.svg.png?20191003091949)
Original file (SVG file, nominally 800 × 600 pixels, file size: 27 KB)
Captions
Captions
Summary
[edit]DescriptionVFPt capacitor-infinite-plate uniform.svg |
English: Electric field of simple parallel plate capacitor. The capacitor consists of two parallel rectangular plates perpendicular the the image plane and expanding to infinity. The field is accurately computed for a uniform potential at each plate. The charge density increases towards the edges. |
Date | |
Source | Own work |
Author | Geek3 |
Other versions | VFPt capacitor-infinite-plate.svg, VFPt capacitor-infinite-plate uniform-potential+contour.svg |
SVG development InfoField | ![]() This plot was created with VectorFieldPlot. |
Source code InfoField | Python code# paste this code at the end of VectorFieldPlot 2.4
doc = FieldplotDocument('VFPt_capacitor-infinite-plate_uniform',
width=800, height=600, commons=True)
# capacitor dimensions
l = 4.5
d = 1.5
# To model the real, non-uniform charge distribution on the capacitor plate,
# we we cut the plate into several finite segments and equalize their potential.
nsheets = 10 # caution, increases computing effort a lot.
q_list = sc.ones(nsheets)
# higher segment density towards the edges, where charge density varies more
r_list = l/2. * (1.0 - sc.linspace(1, 0, nsheets + 1)[1:]**2)
for i_iter in range(50):
plates = []
for isheet in range(nsheets):
r = r_list[isheet]
Q = 2. * r * (q_list[isheet])
if isheet < nsheets - 1:
Q -= 2. * r * q_list[isheet + 1]
plates.append({'x0':-r, 'y0':d/2., 'x1':r, 'y1':d/2., 'q':Q})
plates.append({'x0':-r, 'y0':-d/2., 'x1':r, 'y1':-d/2., 'q':-Q})
field = Field([ ['charged_plane', p] for p in plates])
V_list = [field.V([(r_list[0]) / 2., d/2.])]
for i in range(1, nsheets):
V_list.append(field.V([(r_list[i-1] + r_list[i]) / 2., d/2.]))
# We want the potential to be 1 everywhere on the plate,
# so iteratively adapt the charges
q_list = q_list / V_list
print 'segment charge densities', q_list
print 'segment potentials', V_list
Q_list = [q_list[0] * r_list[0]] + [q_list[i] * (r_list[i] - r_list[i-1]) for i in range(1, nsheets)]
charge_sums = sc.cumsum([0.] + Q_list[::-1] + Q_list)
relative_charge_position = ip.interp1d(charge_sums / charge_sums[-1],
list(-r_list[::-1]) + [0.] + list(r_list))
def startpath(t):
# take an oval with stright lines and half-cirles around one plate
tt = (t%1) * (2 * l + pi * d)
if tt <= l*0.5:
return sc.array([tt, d])
elif tt <= l*0.5 + pi/2.*d:
phi = (tt - l*0.5) / (d/2.)
return sc.array([l*0.5 + d*0.5*sin(phi), d*0.5 + d*0.5*cos(phi)])
elif tt <= l*1.5 + pi/2.*d:
return sc.array([l - (tt - pi/2.*d), 0.])
elif tt <= l*1.5 + pi*d:
phi = (tt - l*1.5) / (d/2.)
return sc.array([-l*0.5 + d*0.5*sin(phi), d*0.5 + d*0.5*cos(phi)])
else:
return sc.array([tt - (l*2. + pi*d), d])
nlines = 22
startpoints = Startpath(field, startpath).npoints(nlines)
# plot field lines
for p0 in startpoints:
line = FieldLine(field, p0, directions='both')
doc.draw_line(line, linewidth=2.4, arrows_style={'dist':2, 'min_arrows':1})
# plot capacitor plate
D = 0.055
lw = 0.01
nsign = nlines
plus = 'M 0,-0.02 v 0.04 M -0.02,0 h 0.04'
minus = 'M -0.02,0 h 0.04'
for iplate in range(2):
yplate = d / 2. * {0:-1., 1:1.}[iplate]
M = sc.array([0., yplate])
R = sc.array([l/2., 0.])
a = atan2(R[1], R[0])
if iplate == 1:
col = '#e22'
sign = plus
else:
col = '#45e'
sign = minus
transform = 'translate({:.6g},{:.6g})'.format(M[0], M[1])
transform += ' rotate({:.6g})'.format(degrees(a))
doc.draw_object('rect', {'x':-vabs(R)-D/2., 'width':2*vabs(R)+D,
'y':-D, 'height':2*D,
'style':'fill:{:s}; stroke:#000; stroke-width:{:.6g}'.format(col, lw),
'transform':transform})
for i in range(nsign):
pos = [relative_charge_position((i + 0.5) / nsign), yplate]
doc.draw_object('path', {'d':sign,
'transform':'translate({:.6g},{:.6g})'.format(*pos),
'style':'fill:none; stroke:#000; stroke-width:{:.6g}; '.format(2*lw) +
'stroke-linecap:square'})
doc.write()
|
Licensing
[edit]![w:en:Creative Commons](https://upload.wikimedia.org/wikipedia/commons/thumb/7/79/CC_some_rights_reserved.svg/90px-CC_some_rights_reserved.svg.png)
![attribution](https://upload.wikimedia.org/wikipedia/commons/thumb/1/11/Cc-by_new_white.svg/24px-Cc-by_new_white.svg.png)
![share alike](https://upload.wikimedia.org/wikipedia/commons/thumb/d/df/Cc-sa_white.svg/24px-Cc-sa_white.svg.png)
- 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.
File history
Click on a date/time to view the file as it appeared at that time.
Date/Time | Thumbnail | Dimensions | User | Comment | |
---|---|---|---|---|---|
current | 09:19, 3 October 2019 | ![]() | 800 × 600 (27 KB) | Geek3 (talk | contribs) | User created page with UploadWizard |
You cannot overwrite this file.
File usage on Commons
The following page uses this file:
Metadata
This file contains additional information such as Exif metadata which may have been added by the digital camera, scanner, or software program used to create or digitize it. If the file has been modified from its original state, some details such as the timestamp may not fully reflect those of the original file. The timestamp is only as accurate as the clock in the camera, and it may be completely wrong.
Short title | VFPt_capacitor-infinite-plate_uniform |
---|---|
Image title | VFPt_capacitor-infinite-plate_uniform
created with VectorFieldPlot 2.3 https://commons.wikimedia.org/wiki/User:Geek3/VectorFieldPlot about: https://commons.wikimedia.org/wiki/File:VFPt_capacitor-infinite-plate_uniform.svg rights: Creative Commons Attribution ShareAlike 4.0 |
Width | 800 |
Height | 600 |