A) 9000 N
B) 12000 N
C) 24000 N
D) 36000 N
Correct Answer: B
Solution :
The schematic diagram of distribution of charges on. x-axis is shown in figure Total force acting on 1 C charge is given by \[F=\frac{1}{4\pi {{\varepsilon }_{0}}}\left[ \frac{1\times 1\times {{10}^{-6}}}{{{(1)}^{2}}} \right.+\frac{1\times 1\times {{10}^{-6}}}{{{(2)}^{2}}}\] \[\left. +\frac{1\times 1\times {{10}^{-6}}}{{{(4)}^{2}}}+\frac{1\times 1\times {{10}^{-6}}}{{{(8)}^{2}}}+.....\infty \right]\] \[=\frac{{{10}^{-6}}}{4\pi {{\varepsilon }_{0}}}\left[ \frac{1}{1}+\frac{1}{4}+\frac{1}{16}+\frac{1}{64}+....\infty \right]\] \[=9\times {{10}^{-6}}\times {{10}^{9}}\left( \frac{1}{1-\frac{1}{4}} \right)\] \[=9\times {{10}^{9}}\times {{10}^{-6}}\times \frac{4}{3}\] \[=9\times \frac{4}{3}\times {{10}^{3}}=12000N\]You need to login to perform this action.
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