A method and corresponding apparatus are provided for measuring neutron spin precession in an electric field with high sensitivity suitable for practical applications in non-destructive testing, imaging, and the like. Production of a neutron beam with a polarization vector P is followed by transmitting the spin-polarized neutron beam through a sample region in which there is a target generating an electric field, polarization-analyzing the transmitted neutron beam with an analyzing direction orthogonal to P, detecting an intensity of the polarization-analyzed neutron beam; and mapping the detected neutron-beam intensity to a field-strength value for the target electric field.