Lêer:VFPt metal balls largesmall potential.svg
Oorspronklike lêer (SVG-lêer, normaalweg 800 × 600 piksels, lêergrootte: 156 KG)
Hierdie lêer kom vanaf Wikimedia Commons en kan ook in ander projekte gebruik word. Die beskrywing op die lêer se inligtingsblad word hieronder weergegee.
Opsomming
BeskrywingVFPt metal balls largesmall potential.svg |
English: Electric field around a large and a small conducting sphere at opposite electric potential. The shape of the field lines is computed exactly, using the method of image charges with an infinite series of charges inside the two spheres. Field lines are always orthogonal to the surface of each sphere. In reality, the field is created by a continuous charge distribution at the surface of each sphere, indicated by small plus and minus signs. The electric potential is depicted as background color with yellow at 0V. |
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Datum | |||
Bron | Eie werk | ||
Outeur | Geek3 | ||
Ander weergawes |
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SVG genesis InfoField | This W3C-invalid vector image was created with Inkscape, or with something else.
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Bronkode InfoField | SVG code# paste this code at the end of VectorFieldPlot 1.10
# https://commons.wikimedia.org/wiki/User:Geek3/VectorFieldPlot
u = 100.0
doc = FieldplotDocument('VFPt_metal_balls_largesmall_potential',
commons=True, width=800, height=600, center=[400, 300], unit=u)
# define two spheres with position, radius and charge
s1 = {'p':sc.array([-1.0, 0.]), 'r':1.5}
s2 = {'p':sc.array([2.0, 0.]), 'r':0.5}
# make charge proportional to capacitance, which is proportional to radius.
s1['q'] = s1['r']
s2['q'] = -s2['r']
d = vabs(s2['p'] - s1['p'])
v12 = (s2['p'] - s1['p']) / d
# compute series of charges https://dx.doi.org/10.2174/1874183500902010032
charges = [[s1['p'][0], s1['p'][1], s1['q']], [s2['p'][0], s2['p'][1], s2['q']]]
r1 = r2 = 0.
q1, q2 = s1['q'], s2['q']
q0 = max(fabs(q1), fabs(q2))
for i in range(10):
q1, q2 = -s1['r'] * q2 / (d - r2), -s2['r'] * q1 / (d - r1),
r1, r2 = s1['r']**2 / (d - r2), s2['r']**2 / (d - r1)
p1, p2 = s1['p'] + r1 * v12, s2['p'] - r2 * v12
charges.append([p1[0], p1[1], q1])
charges.append([p2[0], p2[1], q2])
if max(fabs(q1), fabs(q2)) < 1e-3 * q0:
break
field = Field({'monopoles':charges})
# draw potential in background
p_array = sc.array([c[:2] for c in charges])
q_array = sc.array([c[2] for c in charges])
def potential(xy):
return sc.dot(q_array, 1. / sc.linalg.norm(xy - p_array, axis=1))
from matplotlib import colors
# colormap from aqua through yellow to fuchsia
cmap = colors.ListedColormap([sc.clip((2*x, 2*(1-x), 4*(x-0.5)**2), 0, 1)
for x in sc.linspace(0., 1., 2048)])
doc.draw_scalar_field(func=potential, cmap=cmap,
vmin=potential(s2['p'] + s2['r'] * sc.array([1., 0.])),
vmax=potential(s1['p'] + s1['r'] * sc.array([-1., 0.])))
# draw symbols
for c in charges:
doc.draw_charges(Field({'monopoles':[c]}), scale=0.6*sqrt(fabs(c[2])))
gradr = doc.draw_object('linearGradient', {'id':'rod_shade', 'x1':0, 'x2':0,
'y1':0, 'y2':1, 'gradientUnits':'objectBoundingBox'}, group=doc.defs)
for col, of in (('#666', 0), ('#ddd', 0.6), ('#fff', 0.7), ('#ccc', 0.75),
('#888', 1)):
doc.draw_object('stop', {'offset':of, 'stop-color':col}, group=gradr)
gradb = doc.draw_object('radialGradient', {'id':'metal_spot', 'cx':'0.53',
'cy':'0.54', 'r':'0.55', 'fx':'0.65', 'fy':'0.7',
'gradientUnits':'objectBoundingBox'}, group=doc.defs)
for col, of in (('#fff', 0), ('#e7e7e7', 0.15), ('#ddd', 0.25),
('#aaa', 0.7), ('#888', 0.9), ('#666', 1)):
doc.draw_object('stop', {'offset':of, 'stop-color':col}, group=gradb)
ball_charges = []
for ib in range(2):
ball = doc.draw_object('g', {'id':'metal_ball{:}'.format(ib+1),
'transform':'translate({:.3f},{:.3f})'.format(*([s1, s2][ib]['p'])),
'style':'fill:none; stroke:#000;stroke-linecap:square', 'opacity':1})
# draw rods
if ib == 0:
x1, x2 = -4.1 - s1['p'][0], -0.9 * s1['r']
else:
x1, x2 = 0.9 * s2['r'], 4.1 - s2['p'][0]
doc.draw_object('rect', {'x':x1, 'width':x2-x1,
'y':-0.1/1.2+0.01, 'height':0.2/1.2-0.02,
'style':'fill:url(#rod_shade); stroke-width:0.02'}, group=ball)
# draw metal balls
doc.draw_object('circle', {'cx':0, 'cy':0, 'r':[s1, s2][ib]['r'],
'style':'fill:url(#metal_spot); stroke-width:0.02'}, group=ball)
ball_charges.append(doc.draw_object('g',
{'style':'stroke-width:0.02'}, group=ball))
# find well-distributed start positions of field lines
def get_startpoint_function(startpath, field):
'''
Given a vector function startpath(t), this will return a new
function such that the scalar parameter t in [0,1] progresses
indirectly proportional to the orthogonal field strength.
'''
def dstartpath(t):
return (startpath(t+1e-6) - startpath(t-1e-6)) / 2e-6
def FieldSum(t0, t1):
return ig.quad(lambda t: sc.absolute(sc.cross(
field.F(startpath(t)), dstartpath(t))), t0, t1)[0]
Ftotal = FieldSum(0, 1)
def startpos(s):
t = op.brentq(lambda t: FieldSum(0, t) / Ftotal - s, 0, 1)
return startpath(t)
return startpos
startp = []
def startpath1(t):
phi = 2. * pi * t
return (sc.array(s2['p']) + 1.5 * sc.array([cos(phi), sin(phi)]))
start_func1 = get_startpoint_function(startpath1, field)
nlines1 = 16
for i in range(nlines1):
startp.append(start_func1((0.5 + i) / nlines1))
def startpath2(t):
phi = 2. * pi * (0.195 + 0.61 * t)
return (sc.array(s1['p']) + 1.5 * sc.array([cos(phi), -sin(phi)]))
start_func2 = get_startpoint_function(startpath2, field)
nlines2 = 14
for i in range(nlines2):
startp.append(start_func2((0.5 + i) / nlines2))
# draw the field lines
for p0 in startp:
line = FieldLine(field, p0, directions='both', maxr=7.)
# draw little charge signs near the surface
path_minus = 'M {0:.5f},0 h {1:.5f}'.format(-2./u, 4./u)
path_plus = 'M {0:.5f},0 h {1:.5f} M 0,{0:.5f} v {1:.5f}'.format(-2./u, 4./u)
for si in range(2):
sphere = [s1, s2][si]
# check if fieldline ends inside the sphere
for ci in range(2):
if vabs(line.get_position(ci) - sphere['p']) < sphere['r']:
# find the point where the field line cuts the surface
t = op.brentq(lambda t: vabs(line.get_position(t)
- sphere['p']) - sphere['r'], 0., 1.)
pr = line.get_position(t) - sphere['p']
cpos = 0.9 * sphere['r'] * pr / vabs(pr)
doc.draw_object('path', {'stroke':'black', 'd':
[path_plus, path_minus][ci],
'transform':'translate({:.5f},{:.5f})'.format(
round(u*cpos[0])/u, round(u*cpos[1])/u)},
group=ball_charges[si])
arrow_d = 2.0
of = [0.5 + s1['r'] / arrow_d, 0.5, 0.5, 0.5 + s2['r'] / arrow_d]
doc.draw_line(line, arrows_style={'dist':arrow_d, 'offsets':of})
doc.write()
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Lisensiëring
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Items portrayed in this file
uitbeelding
electrostatic induction Engels
some value
copyrighted Engels
source of file Engels
30 Desember 2018
media type Engels
image/svg+xml
Lêergeskiedenis
Klik op die datum/tyd om te sien hoe die lêer destyds gelyk het.
Datum/Tyd | Duimnael | Dimensies | Gebruiker | Opmerking | |
---|---|---|---|---|---|
huidig | 20:05, 30 Desember 2018 | 800 × 600 (156 KG) | Geek3 | User created page with UploadWizard |
Lêergebruik
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Globale lêergebruik
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Metadata
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Kort titel | VFPt_metal_balls_largesmall_potential |
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Beeldtitel | VFPt_metal_balls_largesmall_potential
created with VectorFieldPlot 1.10 https://commons.wikimedia.org/wiki/User:Geek3/VectorFieldPlot about: https://commons.wikimedia.org/wiki/File:VFPt_metal_balls_largesmall_potential.svg rights: Creative Commons Attribution ShareAlike 4.0 |
Breedte | 800 |
Hoogte | 600 |