Measurements of the structure of the electrostatic fields produced by the expansion of a laser-produced plasma into a background magnetized plasma are presented. The three-dimensional measurements of the electrostatic field are made using an emissive probe that measures the time-varying plasma potential on two orthogonal planes, one across and one containing the background magnetic field. The inductive electric field is also calculated from probe measurements of the time-varying magnetic fields. Deviations from local charge neutrality at the level of 10(-4) generate a radial electrostatic field with peak strength an order of magnitude larger than the corresponding inductive field. The electrostatic energy density near full expansion is over an order of magnitude larger than that of the induced azimuthal electric field. These measurements show that electrostatic fields must be included in theoretical and computational models of collisionless coupling in magnetized point explosions of laser-produced plasmas and their relation to similar phenomena such as magnetospheric chemical releases.