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Q.

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 plates is

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a

E1:E2:E3=23:1:23

b

E1:E2:E3=12:1:12

c

and variation of electric potential will be

d

answer is B.

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Detailed Solution

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 symmetryV1−2=V3−4and V2−3=2V2−1=2V4−3because charge capacitor 2-3 is double. Electric field = potential dE1:E2:E3=1:2:1=12:1:12and from plate 1 to 4Potential first increases, then decreases, and again increases.Since we are going first in direction opposite of E and then in direction of E.
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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 plates is