An imaginary cubical surface of side

$$

has its edges parallel to the

$$

$-,$

$$

$-$ and z$-$axes, one corner at the point

$$

$=$

$0$

$,$

$$

$=$

$0$

$,$

$$

$=$

$0$

and the opposite corner at the point

$$

$=$

$$

$,$

$$

$=$

$$

$,$

$$

$=$

$$

$.$

The cube is in a region of uniform electric field

$$

$$

$=$

$$

$1$

$$

$^$

$+$

$$

$2$

$$

$^$

$,$

where

$$

$1$

and

$$

$2$

are positive constants. Calculate the electric flux through $($a$)$ the cube face in the plane

$$

$=$

$0$

$,($b$)$ the cube face in the plane

$$

$=$

$$

$,$

$($c$)$ the cube face in the plane

$$

$=$

$0$

$,($d$)$ the cube face in the plane

$$

$=$

$$

$,$

$($e$)$ the cube face in the plane

$$

$=$

$0$

$,($f$)$ the cube face in the plane

$$

$=$

$$

$,$

and $($g$)$ the entire cubical surface. For each face the normal points out of the cube.