Interpretation
The EFIE describes a radiated field E given a set of sources J, and as such it is the fundamental equation used in antenna analysis and design. It is a very general relationship that can be used to compute the radiated field of any sort of antenna once the current distribution on it is known. The most important aspect of the EFIE is that it allows us to solve the radiation/scattering problem in an unbounded region, or one whose boundary is located at infinity. For closed surfaces it is possible to use the Magnetic Field Integral Equation or the Combined Field Integral Equation, both of which result in a set of equations with improved condition number compared to the EFIE. However, the MFIE and CFIE can still contain resonances.
In scattering problems, it is desirable to determine an unknown scattered field that is due to a known incident field . Unfortunately, the EFIE relates the scattered field to J, not the incident field, so we do not know what J is. This sort of problem can be solved by imposing the boundary conditions on the incident and scattered field, allowing one to write the EFIE in terms of and J alone. Once this has been done, the integral equation can then be solved by a numerical technique appropriate to integral equations such as the method of moments.
Read more about this topic: Electric-field Integral Equation