A charged large metal sheet is placed into uniform electric field, perpendicularly 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)=5xx10^(5)V//m` and on the right it is `E_(2) = 3xx10^(5)V//m`. The sheet experiences a net electric force of 0.08N. Find the area of one face of the sheet. Assume external field to remain constant after introducing the large sheet. `Use (1/(4pivarepsilon_(0)))=9xx10^(9)Nm^(2)//C^(2)`

Options

A. `3.6pixx10^(-2)m^(2)`
B. `0.9pixx10^(-2)m^(2)`
C. `1.8pixx10^(-2)m^(2)`
D. none

Answer

A

Explanation

`E_(1)=sigma_(1)/varepsilon_(0) E_(2)=sigma_(2)/varepsilon_(0)`
`(sigma_(1)^(2)/(2varepsilon_(0))-sigma_(2)^(2)/(2varepsilon_(0)))A=0.08`
`A((E_(1)^(2)varepsilon_(0)^(2))/(2varepsilon_(0))-(E_(2)^(2)varepsilon_(0)^(2))/(2varepsilon_(0)))=0.08`
`Avarepsilon_(0)/2 [25xx10^(10)-9xx10^(10)]=0.08, A=(0.08xx2xx36pixx10^(9))/(16xx10^(10)xx1)=3.6pixx10^(-2)m^(2)`