# Applying Boundary Conditions

Boundary conditions refer to already known properties of the physics of the problem. These help to derive the solvable integral equations.

Boundary conditions differ depending on the problem to be solved. A dielectric body would have different boundary conditions compared to a PEC body. For the arbitrary shaped PEC body shown in Figure 1 the boundary condition states that the electric field tangential to the surface is zero all over the surface. In terms of the incident and scattered fields (Equation 1) we can then write:

(1) ${E}_{scat,\mathrm{tan}}=-{E}_{inc,\mathrm{tan}}$

This equation is also denoted the electric field integral equation (EFIE).

It was previously shown that an integral operation applied to the surface currents leads to the scattered fields. Therefore we can write in simple notation:

(2) $ℒ{\left\{{J}_{scat}\right\}}_{\mathrm{tan}}=-{E}_{inc,\mathrm{tan}}$
where $ℒ$ represents the integral operator and $\left\{{J}_{scat}\right\}$ are the unknown currents to be found.