In this paper we consider an antenna consisting of an infinite plane metallic plate divided into two half planes by an infinitely narrow slit across which an alternating electric field of frequency ω is applied. The antenna is immersed in a cold nonmagnetized plasma. Between the homogeneous plasma and the antenna surface an ion sheath is assumed to be present. The fields are calculated for a given density profile of the electrons by a small signal theory. The electromagnetic energy radiated from the slit is determined for frequencies below the plasma frequency. It is shown that the radiated energy is completely absorbed in the sheath. The radiation admittance is calculated as a function of frequency, the sheath thickness, and the plasma density.