The electric field components in the figure below are `E_(x) = 800 x^(2) N //C ,E_(y)= E_(z) = 0`.
Calculate
(1) The flux throught he cube and
(2) The charge withing the cube
Assume that a =0.1 m

Explanation

(a) Except ABCD surface flux through other surfaces is zero
`phi_("cube") = phi_("ABCD")`
`= 800 a^(2) hat(i) . a^(2) hat(i)`
`= 800 a^(4)`
`= 800 xx ( 0.1)^(4)`
`= 8 xx 10^(2) xx 10^(-4)`
`= 8 xx 10^(-2) N m^(2) //C`
(b) Charge `Q = phi epsilon_(0)= 8 xx 10^(-2) xx 8.854 xx10^(-12) C`
`= 7.08 xx 10^(-13) C`