Two infinite parallel,non- conducting sheets carry equal positive charge density `sigma` ,One is placed on the other at distance `x=a` Take potential `V=0` at `x=0` then

Options

A. For `0 le x le a` potential `V_(x)=0`
B. for `x ge a` potential `V_(x)=(sigma)/(epsilon_(0))(x-a)`
C. for `x ge a` potential `V_(x)=-(sigma)/(epsilon_(0))(x-a)`
D. For `x le a` potential `V_(x)=-(sigma)/(epsilon_(0))x`

Answer

A,B,D

Explanation

`0 lt xlt a`
`V_(x)=[-int_(0)^(x)E_(x)dx]+V_(0)=0(as E_(x)=0)`
`x gea,V_(s)=-int_(0)^(x)E_(x)dx+V_((a))`
` V_(x)=[-int_(a)^(x)(sigma)/(epsilon_(0))dx]+V_((a))=(sigma)/(epsilon_(0))(x-a)=(sigma)/(epsilon_(0))(x-a)`
`x le a,V_(x)=`
`-int_(0)^(x)E_(x)dx+V_((0))[:. E_(x)=(sigma)/(epsilon_(0))]`
`V_((x))=((-sigma)/(epsilon_(0))x)+V_((0))=(sigma)/(epsilon_(0)x)`