Ficheru:VFPt metal balls largesmall potential.svg
Ficheru orixinal (ficheru SVG, 800 × 600 píxels nominales, tamañu de ficheru: 156 kB)
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DescripciónVFPt 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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Data | |||
Fonte | Trabayu propiu | ||
Autor | Geek3 | ||
Otres versiones |
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SVG desarrollo InfoField |
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Códigu fonte 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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Elementos representados en este archivo
representa a
inducción electrostática español
Algún valor sin elemento de Wikidata
CC BY-SA 4.0 español
30 avi 2018
tipo de archivo español
image/svg+xml
Historial del ficheru
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Data/Hora | Miniatura | Dimensiones | Usuariu | Comentariu | |
---|---|---|---|---|---|
actual | 20:05 30 avi 2018 | 800 × 600 (156 kB) | Geek3 | User created page with UploadWizard |
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Metadatos
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Títulu curtiu | VFPt_metal_balls_largesmall_potential |
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Títulu de la imaxe | 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 |
Anchor | 800 |
Altor | 600 |