The quarter‐wave monopole base driven over a circular ground plane with a finite radius has applications in over‐the‐horizon radar and on surveillance aircraft. A new use, for which the analysis is given in this paper, is as an over‐the‐head‐mounted antenna for cellular telephones. With this design, the electromagnetic field in the head and the associated specific absorption rate of electromagnetic energy are greatly reduced when compared with the conventional hand‐held transceiver. A complete analysis is carried out of the electromagnetic field on the surface of the head and throughout its interior when the head is modeled as a cylinder with the electrical properties of the brain enclosed in a wall with the thickness and electrical properties of the skull. Graphs and tables are provided that give the field in the air on the surface of the head and in the skull and brain. The far field is also determined. The results are compared with those obtained with the hand‐held radiotelepho