An infinite number of electric charges each equal to 5 nano coulombs are placed along x-axis at x = 1 cm, x-2 cm, x -4 cm, x = 8 cm,.. and so on. In this setup, if the consecutive charges have opposite sign, then the electric field in newton/coulomb at x =0 is

Options

A. `12 xx 10^(4)`
B. `24 xx 10^(4)`
C. `36 xx 10^(4)`
D. `48 xx 10^(4)`

Answer

( c)

Explanation

Resultant Electric field,
`E = E_(1) + E_(2) + E_(3) + ……..`
`1/4pi epsilon_(0)[Q_(1)/(r_(1))^(2) - Q_(2)/(r_(2))^(2) + …...]`
` = 1/4 pi epsilon_(0)[Q/(1 xx 10^(-2))^(2)+ Q/(2 xx 10^(-2))^(2) + Q/(4 xx 10^(-2))^(2) + ……... ]`
` = 9 xx 10^(9)/10^(-4)[1/1 - (-1/4)]xx 5 xx 10^(-9) = 45/10^(-4) xx 4/5`
` = 36 xx 10^(4) NC^(-1)`