# Electric Fields for Pairs of Cylinders or Spheres

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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.

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Contributed by: Y. Shibuya (August 2012)

Open content licensed under CC BY-NC-SA

## Snapshots

## Details

Snapshot 1: a pair of cylinders, symmetrical field observed for voltage difference

Snapshot 2: a sphere gap, symmetrical field observed for

Snapshot 3: a sphere gap, asymmetrical field observed for (the usual case for high voltage testing, in which one sphere is grounded)

In both cases, the electric field can be calculated from the potential function by .

The energy density is obtainable by .

The potential at any point is expressed as follows:

Pair of Parallel Cylinders

Assuming the line charges are , separated by the length , then , where , are the distances to the line charges. The value of is determined by per-unit-length capacitance .

Pair of Spheres (sphere gap)

Denoting the image charges of order , at shifted positions, , where , are the distances to the image charges. An upper limit of is found satisfactory in all these examples.

References

[1] C. R. Paul, *Analysis of Multiconductor Transmission Lines*, New York: John Wiley & Sons, 1994.

[2] P. T. Metzer and J. E. Lane, "Electric Potential Due to a System of Conducting Spheres," *The Open Applied Physics Journal*, 2, 2009 pp. 32–48. http://benthamopen.com/ABSTRACT/TOAPJ-2-32.

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