An electron beam apparatus and method for testing a circuit. The electron beam apparatus comprises an electron beam incident on an outer surface of an insulating layer overlying one or more electrical conductors of the circuit for generating a time varying or alternating current electrical potential on the surface; and a measurement unit connected to the circuit for measuring an electrical signal capacitively coupled to the electrical conductors to identify and map a conduction state of each of the electrical conductors, with or without an electrical bias signal being applied to the circuit. The electron beam apparatus can further include a secondary electron detector for forming a secondary electron image for registration with a map of the conduction state of the electrical conductors. The apparatus and method are useful for failure analysis or qualification testing to determine the presence of any open-circuits or short-circuits, and to verify the continuity or integrity of electrical conductors buried below an insulating layer thickness of 1-100 .mu.m or more without damaging or breaking down the insulating layer. The types of electrical circuits that can be tested include integrated circuits, multi-chip modules, printed circuit boards and flexible printed circuits.