Two parallel infinite line charges `+lamda and -lamda` are placed with a separation distance R in free space. The net electric field exactly mid-way between the two line charges is

Options

A. zero
B. `(2lambda)/(pi epsilon_(0)R)`
C. `(lambda)/(pi epsilon_(0)R)`
D. `(lambda)/(2 pi epsilon_(0)R)`

Answer

B

Explanation

Electric field at point P due to line charge distribution `+ lambda , E_(+lambda) = (lambda)/(2pi epsilon_(0)((R )/(2)))` away from `+ lambda`
Electric field at point P due to line charge distribution `- lambda`,
`E_(-(lambda)) = (lambda)/(2pi epsilon_(0)((R )/(2)))` towards `-lambda`
`E_(+lambda)` and `E_(-lambda)` have same direction,
`:. E_("net") = E_(+lambda) + E_(+lambda)`
`= 2 ((lambda)/(2pi epsilon_(0)((R )/(2)))) = (2 lambda)/(pi epsilon_(0)R)`