Question

Four large metal plates are given charges as shown in figure. The middle two are then connected through a wire. Find the charge that will flow through the wire:

• A. $5Q$ from A to B
• B. $\frac{5Q}{2}$ from A to B
• C. $5Q$ from B to A
• D. No charge will flow

Answer 1

The correct option is A $5Q$ from A to B

Distribution of charge before the wire is connected is shown in fig. On connecting with the wire, $5Q$ and $-5Q$will get neutralized. Hence, $5Q$ charge will flow from A to B.
let initially there is $x$ charge on the left side of plate 1, therefore on the right side of plate 4 there will also be charge x
left right
plate 1(Q) $x$ $Q-x$
plate 2(2Q) $-(Q-x)$ $2Q+(Q-x)$

plate 3(-3Q) $-[2Q+(Q-x]$ $4Q+x$
plate 4(-4Q) $-4Q-x$ $x$
now total charge on plate 3 should be $-3Q$
$\Rightarrow -[2Q+(Q-x]+4Q+x=-3Q$
$\Rightarrow x=-2Q$