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.

Options

A. `sigma_(1)=Q/A`
B. `sigma_(1)=Q/(2A)`
C. `sigma_(1)=sigma_(2)`
D. `sigma_(3)=Q/A`

Answer

A

Explanation

Initial charge Q will be distributed uniformaly on plate X of surface area A, a plate has 2 surfaces.
`therefore sigma_(1)=(Q)/(2A)`

As plate Y is brough closer, the charge induced on it but here in no effect on the plte X.
Charge on outer surface is
`X=Q/2`

`implies` distribution of charges on X is
`singma_(2)=(Q)/(2A)=sigma_(1)`
When Y is earthed, the new charge distribution will be as shown in the figure

`therefore sigma_(3)=(Q)/(A)`