a$)$ Find the charge density $),,($ zyx

that produces the electric field

$),($ kzjyixgE $++=$

$$

You are at a point $($a$,$ b$,$ c$)$ on the surface

$)\mathrm{.}0()(2/1222=$ zyxrz

Assuming both a and b are positive, in what direction must you move

$($a$)$ so that the rate of change of z will be zero?

$($b$)$ so that the rate of increase of z will be greatest?

$($c$)$ so that the rate of decrease of z will be greatest?where g is a constant.

$($b$)$ Find an electric potential $$ such that $$ is the field E

$$ given in $($a$).$

$($c$)$ Verify that

$0$

$2$