Talaksan:VFPt metal balls largesmall potential+contour.svg
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PaglalarawanVFPt metal balls largesmall potential+contour.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 together with equipotential lines. |
Petsa | |
Pinanggalingan | Sariling gawa |
May-akda | Geek3 |
Iba pang mga bersyon |
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SVG genesis InfoField | |
Source code InfoField | Python code# paste this code at the end of VectorFieldPlot 3.1
# https://commons.wikimedia.org/wiki/User:Geek3/VectorFieldPlot
u = 100.0
doc = FieldplotDocument('VFPt_metal_balls_largesmall_potential+contour',
commons=True, width=800, height=600, unit=u)
# define spheres with position and radius
s1 = {'c':sc.array([-1.0, 0.]), 'r':1.5}
s2 = {'c':sc.array([2.0, 0.]), 'r':0.5}
spheres = [s1, s2]
def U_sphere(sphere, charges):
f = Field([ ['monopole', {'x':c['p'][0], 'y':c['p'][1], 'Q':c['Q']}] for c in charges])
return sc.mean([f.V(sphere['c'] + sphere['r'] * array((cos(phi), sin(phi))))
for phi in sc.linspace(0, 2*pi, 64, endpoint=False)])
def Q_sphere(isphere, charges):
return sum([c['Q'] for c in charges if c['i'] == isphere])
# compute series of charges https://dx.doi.org/10.2174/1874183500902010032
def mirrored_charges(p, Q, isphere, spheres, Qmin):
'''
Recursive function. Returns list of mirrored charges for n spheres
'''
if fabs(Q) < Qmin:
return []
charges = [{'p':p, 'Q':Q, 'i':isphere}]
for i, s in enumerate(spheres):
if i != isphere:
pnew = s['c'] + (p - s['c']) * (s['r'] / vabs(p - s['c']))**2
Qnew = -Q * s['r'] / vabs(p - s['c'])
charges += mirrored_charges(pnew, Qnew, i, spheres, Qmin)
return charges
charges_raw = [mirrored_charges(s['c'], 1., si, spheres, 1e-4) for si,s in enumerate(spheres)]
# Use charge normalization from paper above
# Here one can also solve for charge conditions such as neutrality
matrixU = [ [U_sphere(s, cs) for cs in charges_raw] for s in spheres]
matrixQ = [ [Q_sphere(si, cs) for cs in charges_raw] for si in range(len(spheres))]
U0, U1 = 1., -1
charge_factors = sc.linalg.solve(matrixU, [U0, U1])
for il in range(len(charges_raw)):
for ic in range(len(charges_raw[il])):
charges_raw[il][ic]['Q'] *= charge_factors[il]
charges = [c for cl in charges_raw for c in cl]
charges = sorted(charges, key=lambda x: -fabs(x['Q']))
for si, s in enumerate(spheres):
s['U'] = U_sphere(s, charges)
s['Q'] = Q_sphere(si, charges)
#print('sphere', si, s, 'U =', s['U'], 'Q =', s['Q'])
print('using', len(charges), 'mirror charges.')
field = Field([ ['monopole', {'x':c['p'][0], 'y':c['p'][1], 'Q':c['Q']}] for c in charges])
def pot(xy):
for s in spheres:
if vabs(xy - s['c']) <= s['r']:
return s['U']
return field.V(xy)
doc.draw_scalar_field(func=pot, cmap=doc.cmap_AqYlFs, vmin=U1, vmax=U0)
doc.draw_contours(func=pot, linewidth=1, linecolor='#444444',
levels=sc.linspace(U1, U0, 17)[1:-1])
# draw symbols
#for c in charges:
# doc.draw_charges(Field([ ['monopole', {'x':c[0][0], 'y':c[0][1], 'Q':c[1]}] ]),
# scale=0.6*sqrt(fabs(c[1])))
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), ('#ddd', 0.8),
('#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, s in enumerate(spheres):
ball = doc.draw_object('g', {'id':'metal_ball{:}'.format(ib+1),
'transform':'translate({:.3f},{:.3f})'.format(*(s['c'])),
'style':'fill:none; stroke:#000;stroke-linecap:square', 'opacity':1})
# draw rods
if ib == 0:
x1, x2 = -4.1 - s1['c'][0], -0.9 * s1['r']
else:
x1, x2 = 0.9 * s2['r'], 4.1 - s2['c'][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':s['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))
def startpath1(t):
phi = 2. * pi * t
return s2['c'] + 1.5 * array([cos(phi), sin(phi)])
def startpath2(t):
phi = 2. * pi * t
return s1['c'] + s1['r'] * array([cos(phi), -sin(phi)])
nlines1 = 16
startpoints = Startpath(field, startpath1).npoints(nlines1)
nlines2 = 14
startpoints += Startpath(field, startpath2, t0=0.195, t1=1-0.195).npoints(nlines2)
for ip, p0 in enumerate(startpoints):
line = FieldLine(field, p0, directions='both', maxr=7.,
bounds_func=lambda xy: max([s['r'] - vabs(xy-s['c']) for s in [s1, s2]]))
# 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['c']) < sphere['r'] and
vabs(line.get_position(1-ci) - sphere['c']) > sphere['r']):
# find the point where the field line cuts the surface
t = optimize.brentq(lambda t: vabs(line.get_position(t)
- sphere['c']) - sphere['r'], 0., 1.)
pr = line.get_position(t) - sphere['c']
cpos = (-0.06 + 0.96 * sphere['r']) * vnorm(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 = {'start':0.5 + s1['r'] / arrow_d, 'leave_image':0.45,
'enter_image':0.5, 'end':0.5 + s2['r'] / arrow_d}
ar_st = {'dist':arrow_d, 'offsets':of}
if ip >= nlines1:
ar_st = {'potential':pot, 'at_potentials':[0.55*U0]}
ar_st['scale'] = 1.2
doc.draw_line(line, arrows_style=ar_st)
doc.write()
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Items portrayed in this file
depicts English
creator English
some value
copyright status English
copyrighted English
source of file English
original creation by uploader English
30 Mayo 2020
media type English
image/svg+xml
Nakaraan ng file
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Araw/Oras | Thumbnail | Mga dimensiyon | tagagamit | Kumento | |
---|---|---|---|---|---|
ngayon | 12:37, 30 Mayo 2020 | 800 × 600 (183 KB) | Geek3 | Uploaded own work with UploadWizard |
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Naglalaman ng mga karagdagang impormasyon ang talaksan na ito, marahil nadagdag mula sa kamerang digital o scanner na ginamit upang makalikha o gawing digital ito. Kung nabago ang talaksan mula sa orihinal na katayuan, maaaring hindi maipapakita ng lubusan ang detalye ng binagong larawan.
Maiksing pamagat | VFPt_metal_balls_largesmall_potential+contour |
---|---|
Pamagat ng larawan | VFPt_metal_balls_largesmall_potential+contour
created with VectorFieldPlot 3.1 https://commons.wikimedia.org/wiki/User:Geek3/VectorFieldPlot about: https://commons.wikimedia.org/wiki/File:VFPt_metal_balls_largesmall_potential+contour.svg rights: Creative Commons Attribution ShareAlike 4.0 |
Haba | 800 |
Taas | 600 |