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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 NThe 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»

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].



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