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. `(2lamda)/(pi epsilon_(0)R)`
C. `(lamda)/(pi epsilon_(0)R)`
D. `1/(2 pi epsilon_(0)R)`

Answer

B

Explanation

According to gauss.s theorem
`oint E. ds. =(q_("in"))/(epsilon_(0))`
`E.2 pi R xxl=(lamda)/(epsilon_(0))`
`E=1/(2pi) (lamda)/(epsilon_(0)(R//2))xx2=(2 lamda)/(pi epsilon_(0)R)`