Electrostatics Question 223
Question: An infinite number of charges, each of charge 1 mC, are placed on the x-axis with co-ordinates x = 1, 2, 4, 8, ….¥. If a charge of 1 C is kept at the origin, then what is the net force acting on 1 C charge [DCE 2004]
Options:
A) 9000 N
B) 12000 N
C) 24000 N
D) 36000 N
Show Answer
Answer:
Correct Answer: B
Solution:
The schematic diagram of distribution of charges on x-axis.
Total force acting on 1 C charge is given by
$ F=\frac{1}{4\pi {\varepsilon _{0}}}[ \frac{1\times 1\times {{10}^{-6}}}{{{(1)}^{2}}}+\frac{1\times 1\times {{10}^{-6}}}{{{(2)}^{2}}} . $
$ . +\frac{1\times 1\times {{10}^{-6}}}{{{(4)}^{2}}}+\frac{1\times 1\times {{10}^{-6}}}{{{(8)}^{2}}}+….\infty ] $
$ =\frac{{{10}^{-6}}}{4\pi {\varepsilon _{0}}}( \frac{1}{1}+\frac{1}{4}+\frac{1}{16}+\frac{1}{64}+…\infty )=9\times 10^{9}\times {{10}^{-6}}( \frac{1}{1-\frac{1}{4}} ) $
$ =9\times 10^{9}\times {{10}^{-6}}\times \frac{4}{3}=9\times 10^{3}\times \frac{4}{3} $ = 12000 N
