Question

A 1C charge is placed at the origin. Other infinite numbers of unit charges are placed at √2, √4, √8, √16,….(up to infinite) distances from the origin in a straight line. What will be the total force acting on the 1^st charge?

(a) 9*10^9 N

(b) 18*10^9 N

(c) Infinite

(d) 1 N

The question was posed to me in unit test.

The origin of the question is Forces Between Multiple Charges topic in chapter Charges and Fields of Physics – Class 12

Answer 1

Right choice is (a) 9*10^9 N

To explain: The force on 1^st charge will be = 9*10^-9*(\(\frac {1}{\sqrt{2}^2} + \frac {1}{\sqrt{4}^2} + \frac {1}{\sqrt{8}^2}\) +⋯) = 9*10^-9*\(\frac {\frac {1}{2}}{1-\frac {1}{2}}\) = 9*10^-9N [infinite GP formula].