The influence of electric fields on lamellar block copolymer microstructure is studied in the context of a density functional model and its sharp interface limit. A free boundary problem for domain interfaces of strongly segregated polymers is derived, which includes coupling of interface and electric field orientation. The linearized dynamics of lamellar configurations is computed in this context, leading to quantitative criteria for instability as a function of pattern wavelength, field magnitude, and orientation. Numerical simulations of the full model in two and three dimensions are used to study the nonlinear development of instabilities. In three dimensions, sufficiently large electric field magnitude always leads to instability. In two dimensions, the field has either stabilizing or destabilizing effects depending on the misorientation of the field and pattern. Even when linear instabilities are present, the dynamics can lead to stable corrugated domain interfaces which do not align with the electric field. Sufficiently high field strengths, on the other hand, produce topological rearrangement which may lead to alignment.