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 5-5-2019]

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 :

At \[P,\text{ }E={{E}_{1}}+{{E}_{2}}=\frac{2k{{\lambda }_{1}}}{R}+\frac{2k{{\lambda }_{2}}}{R}\] \[\therefore {{\lambda }_{1}}={{\lambda }_{2}}\]             \[\frac{4K\lambda }{R}=\frac{\lambda }{\pi {{\in }_{0}}R}\]