An infinite number of charges, each of coulomb, are placed along x-axis at `x = 1m, 3m, 9m` and so on. Calculate the electric field at the point x = 0 due to these charges if all the charges are of the same sign.

Explanation

Here, `r_(1) = 1m, r_(2) = 3m, r_(3) = 9m`
Electric field,
`E = (q)/(4pi in_(0)) [(1)/((1)^(2))+ (1)/((3)^(2)) + (1)/((9)^(2)) + ..] = (q)/(4 pi in_(0))[(1)/(1 - (1)/(9))] = (q)/(4 pi in_(0)) xx (9)/(8) " " { " using " S_(oo) = (a)/(1 -r)}`
`= (1)/(4pi in_(0)).(9q)/(8) NC^(-1)`