question_answer

A charge +q fixed at each of the points \[x={{x}_{0}},x=3{{x}_{0}},x=5{{x}_{0}}....\] up to \[\infty \] on X-axis and charge -q is fixed on each of the points \[x=2{{x}_{0}},x=4{{x}_{0}},....\] up to \[\infty \]. Here \[{{x}_{0}}\] is a positive constant. Take the potential at a point due to a charge Q at a distance r form it to be \[\frac{Q}{4\pi {{\varepsilon }_{0}}r},\] then the potential at the origin due to above system of charges will be:

A) zero      

B) infinite

C) \[\frac{q}{8\,\pi \,{{\varepsilon }_{0}}{{x}_{0}}\,{{\log }_{e}}\,2}\]

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