Three infinite long plane sheets carrying uniform charge densities `sigma_(1)=-sigma,sigma_(2)=+2sigma and sigma_(3)=3sigma` are placed parallel to the x-z plane at `y=a,y=3a and y=4a` as shown in the figure. What is the electric field at point 'P' ?

Options

A. zero
B. `-(2sigma)/(epsi_(0))hatj`
C. `-(3sigma)/(epsi_(0))hatj`
D. `(3sigma)/(epsi_(0))hatj`

Answer

C

Explanation

The electric field at a point due to an infinitely long plane charged sheet, having a uniform charge density `sigma` is `E=(sigma)/(2epsi_(0))`
If `sigma` is +ve,, then the direction of E is perpendicular to the sheet and away from the sheet and if `sigma` is -ve, it is towards the sheets. using this we find that all the three plates will produce the electric fields at P and they will be directed along the -ve y-axis. hence the net electric field.
`vecE_(P)=vecE_(1)+vecE_(2)+vecE_(3)`
`=[(sigma)/(2peis_(0))+(2sigma)/(2epsi_(0))+(3sigma)/(2epsi_(0))](-hatj)`
`=-(3sigma)/(epsi_(0))hatj`