question_answer

There is an infinite straight chain of alternating charges q and -q. The distance between the two neighboring charges is equal to a. Find the interaction energy of any charge with all the other charges.

A) \[-\frac{2{{q}^{2}}}{4\pi {{\varepsilon }_{0}}a}\]

B) \[\frac{2{{q}^{2}}{{\log }_{e}}2}{4\pi {{\varepsilon }_{0}}a}\]

C) \[-\frac{2{{q}^{2}}{{\log }_{e}}2}{4\pi {{\varepsilon }_{0}}a}\]

D) Zero

Correct Answer: C

Solution :

[c] \[U=2k{{q}^{2}}\left[ -\frac{1}{a}+\frac{1}{2a}-\frac{1}{3a}+\frac{1}{4a}+..... \right]\]