X and Y are large, parallel conducting plates closed to each other. Each face has an area A. X is given a charge Q. Y is without any charge. Points A, B and C are as shown in figure.

If a large conducting plate is given a charge +Q it is distributed equally on both surfaces.

Charge density on both the surfaces is, $\mathrm{\sigma }=\frac{\mathrm{Q}}{2\mathrm{A}}$

So the electric field on both sides of A and B of the plane X is

${\mathrm{E}}_{\mathrm{A}}={\mathrm{E}}_{\mathrm{B}}=\frac{\sigma }{{\mathrm{\epsilon }}_0}=\frac{\mathrm{Q}}{2\mathrm{A}{ϵ}_0}$

If another uncharged plate is placed in front of charged sheet, an equal and opposite charge $-\frac{\mathrm{Q}}{2}$is induced on inner surface and $+\frac{\mathrm{Q}}{2}$ on outer surface. 

So, ${\mathrm{E}}_{\mathrm{C}}=\frac{\mathrm{Q}}{2{\mathrm{AE}}_0}$

i.e ${\mathrm{E}}_{\mathrm{A}}={\mathrm{E}}_{\mathrm{B}}={\mathrm{E}}_{\mathrm{C}}=\frac{\mathrm{Q}}{2{\mathrm{Aϵ}}_0}$

The direction of ${\mathrm{E}}_{\mathrm{A}},{\mathrm{E}}_{\mathrm{B}} \mathrm{and} {\mathrm{E}}_{\mathrm{C}}$ are shown in the figure.