A method for calculating electric field having contributions of an incident electric field from a source and an electric field emitted from another object distinct from the source but in a path of the incident electric field, which is often termed a “scatterer”. This method is formed by a new single-source integral equation which represents the electric field inside the scatterer as a superposition of spherical waves emanating from its boundary. Calculation of electric field using this method is particularly but not exclusively suited for applications such as fault detection in simulations of power systems, remote sensing of stratified structures such as ice, and circuit design concerning chips in electronic packages on circuit boards.