A parallel electric field imposes a distinct signature on the characteristics of particles on the magnetic field line. An analysis is made of particle trajectories in phase space for a steady state collisionles plasma, and it is shown that there are two different ways to infer the potential distribution from particle measurements. The first method invokes quasi-neutrality and is a generalization of work by Alfv¿n and F¿lthammar (1963). An expression is obtained relating the potential distribution, and hence the electric field, to an integral involving the distribution functions of the ions and the electrons. As an example of this method the potential distribution produced by a monoenergetic beam in a Maxwellian plasma is obtained. The second method makes use of the fact that the structure of the apparent loss or source cone is altered by a parallel electric field. There should be observable discontinuities between different regions of phase space because of the fact that the plasmas in these regions have different sources. The shape of the boundary between these regions can be used to infer the potential distribution. An example is given of the effect of a Gaussian electric field with characteristics similar to the potential distribution discussed by Evans (1974). Neither method can be used to infer the potential distribution within a thin region of a few Debye lengths in extent, such as a double layer. However, the second method can be used to infer the location and the potential drop associated with such a double layer.