An infinite number of electric charges each equal to `5` nano-coulomb (magnitude) are placed along `X`-axis at `x=1 cm, x=2 cm,x=8cm`……and so on. In the setup if the consecutive charges have opposite sign, then the electrical field in Newton/Coulomb at `x=0` is `(1/(4piepsilon_(0))= 9xx10^(9)N-m^(2)//C^(2))`

Options

A. `12 xx10^4`
B. `24 xx10^4`
C. `36 xx10^4`
D. `48 xx10^4`

Answer

C

Explanation

`E_0=q/(4piepsilon_0)[1/((10^(-2))^(2))-1/((2xx10^(-2))^2)+1/(4xx10^(-2))^(2)-1/(8xx10^(-2))^(2)]`
`=q/(4piepsilon_0xx10^(-4))[1-1/4+1/16-1/64+.....]`
`=q/(4piepsilon_0xx10^(-4))[(1+1/16+.....)-(1/4+1/64+....)]`
`=(9xx10^9xx5xx10^(-9))/(10^(-4))[(1/(1-1/16))-1/4 (1+1/16+.....)]`
`=45 xx10^4 [(16)/15 -1/4 xx16/15] =45 xx10^4 xx4/5`
`=36 xx10^4 N//C`