The electricfield inside a board

[axcelenator]

a board charged with superficial density σ is in YZ and X=0. another board with a thickness of D(0<X<D) sticks to him with a volumed density ρ(x,y,z)=μ*X. The electric field out of the charged area is zero.
I have to find the elec field inside the board:i made a little gauss cylinder inside the board and outdise him. and so the answer is: E=-2∏Kμ(D^2 - X^2). but, why don't I add to that expresion the electric field of the board chaged with σ? (2∏Kσ)

My second quetion if I have to find the difference between the potentials between (2D,0,0) and (-2D,0,0) what should I do If the elec field is 0 in this areas?

 

[Nate810]

The difference in potentials between (2D,0,0) and (-2D,0,0) is zero since the electric field is zero in those regions. You don't need to add the electric field of the charged board to the expression for the electric field inside the board because the electric field of the charged board is outside the board and does not contribute to the electric field inside the board.