Two infinite, parallel, nonconducting sheets carry equal positive charges density `sigma`. One is placed in the yz plane and the other at distance `x = a`. Take potential `V = 0` at `x = 0`. Then.

Options

A. For `0 lt x lt a`, potential `V = 0`.
B. For `x gt a`, potential `V = -(sigma)/(in_(0))(x-a)`
C. For `x gt a`, potential `V = (sigma)/(in_(0))(x-a)`
D. For `x lt 0` potential `V = (sigma)/(in_(0))x`

Explanation

`0ltxlta:V=[-int_(0)^(x)E_(x)dx]+V_((0))" "=0`(as `E_(x)=0`)
`xgta,V=-int_(a)^(x)E_(x)dx+V_((a))" "=[-int_(a)^(x)(sigma)/(in_(0))dx]+V_((a))=-(sigma)/(in_(0))(x-a)`
`xlt0,V=-int_(0)^(x)E_(x)dx+V_((0))" "=-(-(sigma)/(in_(0)).x)+V_((0))=(sigma)/(in_(0)).x`