Two parallel infinite line charges with linear charge densities `+lambda C//m` and `-lambda` C/m are placed at a distance of 2R in free space. What is the electric field mid-way between the two line charges?

Options

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

Answer

D

Explanation

Electric field due to an infinite line charge, `E = (lambda)/(2pi epsilon_(0)r)`
Net electric field at mid-point O,
`vec(E)_(0) = vec(E)_(1) + vec(E)_(2)`
As, `E_(1) = E_(2) = (lambda)/(2pi epsilon_(0)R)`
`:. E_(0) = 2E_(1) = (lambda)/(pi epsilon_(0)R) NC^(-1)`