Electric Fields for Pairs of Cylinders or Spheres

configuration

pair of cylinders

pair of spheres

voltage

V

1

(V)

1000

voltage

V

2

(V)

0

gap length g (m)

FE`len$$819069981004757911271061495072546797509

cylinder/sphere radius R (m)

FE`R$$819069981004757911271061495072546797509

Electric fields for either a pair of parallel cylinders or a pair of spheres (a sphere gap) are calculated and plotted. The radii of the two cylinders or spheres are assumed to be same.

For a pair of parallel cylinders, the electric field is equivalent to that of parallel line charges with a separation distance

d=2

2

(g/2+R)

-

2

R

, where

g

is the gap length and

R

is the common cylinder radius.

For a pair of spheres (sphere gap), the electric field can be calculated analytically using bispherical coordinates. However, it is far simpler to use the image method, which is applied here.

In both cases, the gap length

g

and radius

R

are selected as the configuration parameters. You can set the voltages of the conductors

V

1

and

V

2

using the sliders.

An asymmetric field appears in the sphere gap case if the applied voltage is not symmetrical (i.e.

V

1

≠-

V

2

). However, in the cylinder system, the field is always symmetrical since the potentials of the cylinders extend to infinity.