Answer to Question #265499 in Field Theory for Aliyu

Question

Find the divergence of the following vector feild.

(i) 3xi+(y-3)j+(2-z)

(ii) Zxi+Xyj+Yzk

Answer 1

The divergence of the vector feild $\bf A$ is defined as

$${\rm div} {\bf A}=\frac{\partial A_x}{\partial x}+\frac{\partial A_y}{\partial y}+\frac{\partial A_z}{\partial z}$$

Hence

(i)

$${\rm div} {\bf A}=\frac{\partial (3x)}{\partial x}+\frac{\partial (y-3)}{\partial y}+\frac{\partial (2-z)}{\partial z}=3$$

(ii)

$${\rm div} {\bf A}=\frac{\partial (zx)}{\partial x}+\frac{\partial (xy)}{\partial y}+\frac{\partial (yz)}{\partial z}=z+x+y$$