question_answer

Two parallel infinite line charges with linear charge densities +λ C/m and –λ C/m are placed at a distance of 2R in free space. What is the electric field mid-way between the two line charges?                                 [NEET 2019]

A) \[\frac{\lambda }{\pi {{\in }_{0}}R}N/C\]

B) \[\frac{\lambda }{2\pi {{\in }_{0}}R}N/C\]

C) Zero     

D) \[\frac{2\lambda }{\pi {{\in }_{0}}R}N/C\]

Correct Answer: B

Solution :

[b]

At \[P,\text{ }E={{E}_{1}}+{{E}_{2}}=\frac{2k{{\lambda }_{1}}}{R}+\frac{2k{{\lambda }_{2}}}{R}\]

\[\therefore {{\lambda }_{1}}={{\lambda }_{2}}\]

\[\frac{4K\lambda }{R}=\frac{\lambda }{\pi {{\in }_{0}}R}\]