There exist electric field in space such that potential gradient along y-axis and z-axis is zero. Figure shows variation of potential with x coordinate. It implies that there should be

Options

A. An infinite long line charge parallel to z-axis at `x=2a` with linear charge density `lamda=(3V_(0)epsilon_(0))/(2a)`
B. An infinite large sheet parallel to yz plane at `x=2a` with surface charge density `sigma=(V_(0)epsilon_(0))/(2a)`
C. An infinite large sheet parallel to yz plane at `x=2a` withh surface charge density `sigma=(V_(0)epsilon_(0))/(a)`
D. An inifinite large sheet parallel to yz plane at `x=2a` with surface charge density `sigma=(3V_(0)epsilon_(0))/(2a)`

Answer

D

Explanation

`xlt2a` `E=(V_(0))/(2a)`
`xge2a` `E=(V_(0))/(a)`

Gauss law for cylindrical
`(V_(0))/(2a)A+(V_(0))/(a)A=(sigmaA)/(epsilon_(0))`
`sigma=(3V_(0)epsilon_(0))/(2a)`