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We know, electric field, E, due to an infinite plate (length>>thickness) having surface charge density
= 
.
(To note: It's independent of distance from the plate and same everywhere!)
In the region outside the second plate,
Since both plates have the same surface charge density(in magnitude only), their electric fields are same in magnitude in this region but opposite in direction.
(E due to positive plate away from it and E due to negative plate towards it!)
Hence, Electric field in the outer region of the second plate is Zero.