Two conducting paltes X and Y ech having large surface area A (on one side) are placed parallel to each other as shown in figure. The platr X is given a charge Q whereas the other is nuetral. Find A)the surface charge density at the inner surface of the plate X. B) the electric field at a pont to the left of the plates, C) the electric field at a point in between the plates asnd d) ther electric field at a point to the right of the plates.

 i am assuming that the area of both the sides are equal  assuming

charge on outer side of the x to be q1   and on the inner side of q-q1

charge on the inner side of  y  is -(q-q1)    because if we draw a gaussian surface passing thru the conductore the electric field inside should be -(coz of conduction properties)

charge on outer side=q-q1

the electric field at any pnt x or y =0 as it is inside the conductor

so        

so  q-q1=q  solving we get   q1=q2

so now we can get the all the answers easily 

Since charge q is distributedon metallic plate, so the charge distributes as q/2 & q/2

            =>       = q/2A

Now E due to metallic face  =   / ₀

By induction of charge -q/2  E due to adjacent face on other metallic plate

      E =   - / ₀

=> E on either side of of plate  =   / ₀ - / ₀   = 0

      E  between plates                 =    / ₀ + / ₀ =  2 / ₀