Three infinitely long charge sheets are placed as shown in figure. The electric field at point P is

Options

A. `2sigma//epsilon_0hatk`
B. `4sigma//epsilon_0hatk`
C. `-2sigma//epsilon_0hatk`
D. `-4sigma//epsilon_0hatk`

Explanation

Figure. Shows the electric fields due to the sheets 1,2 and 3 at point P. The direction of electric fields is according to the charge on the sheet (away from positively charged sheet and toward the negatively charged sheet and perpendicular)
The total electric field is
`vecE=vecE_(1)+vecE_(2)+vecE_(3)`
`=E_(1)(khatk)+E_(2)(-hatk)+E_(3)(-hatk)`
`[(sigma)/(2epsilon_(0))+(2sigma)/(2epsilon_(0))+(sigma)/(2epsilon_(0))](-hatk)`
`=(-2sigma)/(epsilon_(0))hatk`