Four identical metallic plates (1, 2, 3 and 4) are arranged in air at same distance d from each other with their outer plates being connected together and earthed. If the plates 2 and 3 are connected with a cell of constant emf E, then ratio of electric fields between the plate is

Plate 2 acquires a net positive charge and 3 acquires a net negative charge.

Due to induction, plate 1 acquires negative charge and plate 4 positive charge. 1 and 4 are equipotential (since they are joined). 

Due to symmetry

$V_{1.2}=V_{3.4}$

and $V_{2.3}=2V_{2.1}=2V_{4.3}$

Because charge capacitor 2-3 is double.

Electric field $=\frac{potential}{d}$

$E_1:E_2:E_3=1:2:1=\frac{1}{2}:1:\frac{1}{2}$

And from plate 1 to 4

Potential first increases, then decreases,  and again increases. Since we are going first in direction opposite of E and then in direction of E.