# Specifying the Relevant Integral Equation

Specify the integral equation by decomposing the fields into two parts.

## Incident and Scattered Fields

Basic laws of physics dictate when an electromagnetic field encounters an object, currents are excited on the object. These currents will subsequently re-radiate. This behaviour is referred to as “electromagnetic scattering”.

## Finding the Incident Field

In RCS applications, the incident field is a plane wave. For example, a plane wave incident from the negative X axis with the electric field z-polarized gives the incident field as:

In antenna problems, the incident field, also denoted the “excitation,” is usually a
voltage source. A simple form of excitation is the “delta-gap” feed. For an impressed
voltage *V* at the terminals of an antenna over a gap of length δ the incident field can be written as:

If this feed is applied to a wire, the length of the gap is typically the length of a wire segment. Other types of incident fields are magnetic frills and elementary Hertzian dipoles.

## Finding the Scattered Fields

To find the scattered fields an integral equation is applied to the surface currents. This is written in a simple notation as follows: $\mathcal{L}\left\{{J}_{scat}\right\}$ where $\mathcal{L}$ represents the integral operator and $\left\{{J}_{scat}\right\}$ are the unknown currents to be found.