When a charge of amount $Q$ is given to an isolated metal plate $X$ of surface area $A$, its surface charge density becomes ${\sigma }_1$. When an isolated identical plate $Y$ is brought close to $X$ the surface charge density on $X$ becomes ${\sigma }_2$. When $Y$ is earthed the surface charge density on $X$ becomes ${\sigma }_3$. Choose the incorrect option.

Initially charge $Q$ will be distributed uniformly on plate $X$ of surface area $A$, a plate has $2$surfaces.

$\therefore {\sigma }_1=\frac{Q}{2A}$    

As plate $Y$ is brought closer, the charge is induced on Y but there will be no effect on the plate  $X$.

Charge on outer surface of $X$ is $\frac{Q}{2}$.

$\Rightarrow$ Distribution of charges on $X$ is

${\sigma }_2=\frac{Q}{2A}={\sigma }_1$

When Y is earthed, the new charge distribution will be as shown in the figure. the total charge on X will come onto the side nearest to Y.

$\therefore {\sigma }_3=\frac{Q}{A}$