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(B) The total force $F$ acting on the $1 \, C$ charge at the origin due to the infinite series of charges is given by Coulomb's Law:$F = \sum_{i=0}^{\

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$12000$

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(B) The total force $F$ acting on the $1 \, C$ charge at the origin due to the infinite series of charges is given by Coulomb's Law:$F = \sum_{i=0}^{\infty} \frac{k q_1 q_2}{r_i^2} = \frac{1}{4\pi \varepsilon_0} \left( \frac{1 	imes 10^{-6} 	imes 1}{1^2} + \frac{1 	imes 10^{-6} 	imes 1}{2^2} + \frac{1 	imes 10^{-6} 	imes 1}{4^2} + \frac{1 	imes 10^{-6} 	imes 1}{8^2} + ... \infty ight)$$F = (9 	imes 10^9) 	imes 10^{-6} \left( 1 + \frac{1}{4} + \frac{1}{16} + \frac{1}{64} + ... \infty ight)$The term in the bracket is an infinite geometric progression with first term $a = 1$ and common ratio $r = 1/4$. The sum is $S = \frac{a}{1-r} = \frac{1}{1 - 1/4} = \frac{1}{3/4} = \frac{4}{3}$.$F = 9 	imes 10^3 	imes \frac{4}{3} = 3 	imes 10^3 	imes 4 = 12000 \, N$.

An infinite number of charges,each of charge $1 \,\mu C$,are placed on the $x$-axis at coordinates $x = 1, 2, 4, 8, ... \infty$. If a charge of $1 \, C$ is kept at the origin,what is the net force acting on the $1 \, C$ charge in Newtons?

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