The static electric field distribution between two semi-infinite circular cylinders: A model for the feed gap field of a dipole antenna

The static electric field distribution in the gap between two solid perfectly conducting semi-infinite cylinders is obtained in terms of a Fourier-Bessel eigenfunction series. For dipole antennas whose cylinder diameter
2a
and gap length
2d
are both much less than the operating wavelength
\lambda
, this field can serve as the quasistatic excitation field in the gap of the dipole. However, the Fourier-Bessel series is slowly convergent. It is transformed into a rapidly convergent series of ultrasphetical polynomials whose weighting function explicitly satisfies the Meixner edge condition. Numerical results are presented graphically for both the axial electric field on the gap surface and the associated potential distribution. Gap ratios of
d/a
from 0.01 to 10.0 are considered and it is shown that as
d/a \rightarrow 0
the solution approaches the two-dimensional solution obtainable by conformal mapping.