Читать книгу RF/Microwave Engineering and Applications in Energy Systems - Abdullah Eroglu - Страница 42

The divergence theorems states that the volume integral of the divergence of a vector is equal to the surface integral of the same vector enclosing that volume. It is mathematically given by

(1.67)

While this theorem can be applied for an electric flux density, it is valid for any vector. When there are adjoining incremental small volumes, an arbitrary shape is considered to form a larger volume which is enclosed by surface S. Then, flux leaving incremental volume enters the adjacent incremental volume, as shown in Figure 1.16 [1]. Hence, the net flux contribution for a surface integral due to interior surfaces is zero. The contributions that are nonzero occur only for the surfaces enclosing the outer surface of the volume.

Figure 1.16 Illustration of divergence theorem.