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. `(lamda)/(2pi epsilon_0R)N//C`
B. Zero
C. `(lamda)/(pi epsilon_0R)N//C`
D. `(2lamda)/(pi epsilon_0R)N//C`

Answer

D

Explanation

`vecE` due to infinite line charge `=(2klamda)/R`

`lamda` = Charge density
`vecE=vecE_1+vecE_2=(2klamda)/R+(2klamda)/R=(lamda)/(pi epsilon_0R)N//C`