question_answer

A charge \[+q\] is fixed at each of the points \[x={{x}_{0}},\,x=3{{x}_{0}},\,x=5{{x}_{0}}\]..... infinite, on the \[x-\]axis and a charge \[-q\]  is fixed at each of the points \[x=2{{x}_{0}},\,x=4{{x}_{0}},x=6{{x}_{0}}\],..... infinite. Here \[{{x}_{0}}\] is a positive constant. Take the electric potential at a point due to a charge \[Q\] at a distance \[r\] from it to be \[Q/(4\pi {{\varepsilon }_{0}}r)\]. Then, the potential at the origin due to the above system of charges is                                                                         [IIT 1998]

A)                    0                                        

B)            \[\frac{q}{8\pi {{\varepsilon }_{0}}{{x}_{0}}\ln 2}\]

C)                    \[\infty \]                       

D)            \[\frac{q\ln 2}{4\pi {{\varepsilon }_{0}}{{x}_{0}}}\]