A large charged metal sheet is placed in a uniform electric field, perpendicular to the electric field lines. After placing the sheet into the field, the electric field on the left side of the sheet is `E_1 = 5 xx 10^5 Vm^(-1)` and on the right it is `E_2 = 3 xx 10^5 V m^(-1)`. The sheet experiences a net electric force of 0.08 N. Find the area of one face of the sheet. Assume the external field to remain constant after introducing the large sheet. Use
`(1/(4piepsilon_0)) = 9 xx 10^(9) Nm^(2)C^(-2)`

Options

A. `3.6 pi xx 10^(-2)m^(2)`
B. `0.9pi xx 10^(-2)m^(2)`
C. `1.8 pi xx 10^(-2)m^(2)`
D. none of these

Answer

A

Explanation

Let external field be `E_(0)` and surface charge density of sheet be `sigma` (including both surfaces).
`E_(p)=(sigma)/(2epsilon_(0))`
Electric field due to sheet
`E_(1)=E_(0)-E_(p)` (i)
`-E_(2)=E_(0)+E_(p)` (ii)
From (i) and (ii), `E_(0)==(E_(1)-E_(2))/(2)=10^(5)Vm^(-1)`
and `E_(p)=(-E_(1)-E_(2))/(2)=-4xx10^(5)Vm^(-1)`
`(sigma)/(2epsilon_(0))=-4xx10^(5)` or `sigma=-8epsilon_(0)xx10^(5)`
Force on sheet:
`F=qE_(0)` or `0.08=sigmaAE_(0)`
or `0.08=8epsilon_(0)xx10^(5)Axx10^(5)`
or `A=(10^(-12))/(epsilon_(0))=10^(-12)xx36xx10^(9)pi=3.6pixx10^(-2)m^(2)`