Field intensification and emitting area are determined for a spheroid and a whisker-shaped protrusion. The effects of an inhomogeneous field around a protrusion on the transmission coefficient for field emission are computed, and examples are given. The resistive heating of an emitter is analyzed for a case in which both the resistivity and the emission are temperature dependent. An instability is pointed out, and the external resistance which stabilizes the emission of a whisker is given. The spreading of the emitted beam due to field distortion at the protrusion and to spacecharge repulsion is computed separately and given in general form. It is concluded that the beam spreads faster than previous hypotheses assume. The formation of small craters at the anode byssingle electron beams is questioned.