An infinite number of charges, each of charge 1 μC 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?

12000 N

Electric field at the origin is $ E = \frac{q}{4\pi\epsilon_0}(\frac{1}{r_1^2}+ \frac{1}{r_2^2}+.....) = 10^{-6}\times 9\times 10^9 (\frac{1}{1^2}+\frac{1}{2^2}+\frac{1}{4^2}+...) = 9\times 10^3 (\frac{1}{1}+\frac{1}{4}+\frac{1}{16}+...) =\frac{9\times 10^3}{\frac{1}{1-1/4}} = 12000N/C $

Force = qE = 12000N