  We present an experimental analysis of force noise caused by stray
electrostatic fields acting on a charged test mass inside a conducting
enclosure, a key problem for precise gravitational experiments. Measurement of
the average field that couples to test mass charge, and its fluctuations, is
performed with two independent torsion pendulum techniques, including direct
measurement of the forces caused by a change in electrostatic charge. We
analyze the problem with an improved electrostatic model that, coupled with the
experimental data, also indicates how to correctly measure and null the stray
field that interacts with test mass charge. Our measurements allow a
conservative upper limit on acceleration noise, of 2 fm/s$^2$\rthz\ for
frequencies above 0.1 mHz, for the interaction between stray fields and charge
in the LISA gravitational wave mission.
