In this paper the antenna of a traveling wave, which represents a column of isotropic plasma or the plasma column, placed in an external infinitely large magnetic field is studied both theoretically and numerically and compared between them. Plasma is assumed cold and collisionless. The dependence of radiation patterns upon plasma density, geometric parameters of plasma cylinder and radiation wavelength is investigated. At that it is considered not only linear, but also short-wave antenna radiating wavelengths close to the antenna radius. In an isotropic plasma column (B₀ = 0) and in the magnetized (B₀ = ∞), there are only a slow plasma E-wave with frequencies lower the plasma frequency. We study axially symmetric E-wave. Solutions of the dispersion equations give the dependence of the frequency on the wavevector, necessary to calculate the radiation patterns. The wave in plasma cylinder induces a wave of current density. Knowing the current it is possible to calculate the radiation field in the far field and, accordingly, the normalized radiation pattern.