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

Options

A. `(-4 sigma)/(in_(0) hat(k)`
B. `(4 sigma)/(in_(0) hat(k)`
C. `(-2 sigma)/(in_(0) hat(k)`
D. `(2 sigma)/(in_(0) hat(k)`

Answer

C

Explanation

For infinitely chared plane sheet, electric field is given by `E = (sigma)/(2 in_(0))`
Due to charge `+sigma, E_(1) = (sigma)/(2 in_(0))`, downwards
Due to charge `-2 sigma, E_(2) = (2 sigma)/(2 in_(0))`, downwards
Due to charge `-sigma, E_(3) = (sigma)/(2 in_(0))`, downwards
`:.` Total electric field at `P`.
`P = (sigma)/(2 in_(0)) + (2sigma)/(2in_(0)) + (sigma)/(2 in_(0)) = (2 sigma)/(in_(0))`,downwards
`:. vec(E) = - (2sigma)/(in_(0)) hat(k)`