Infinite charges of magnitude `q` each are lying at `x= 1,2,4,8….meter` on `X`-axis. The value of intensity of electric field at point `x=0` due to these charges will be

Options

A. `12 xx10^9 q N//C`
B. Zero
C. `6xx10^9 qN//C`
D. `4xx10^9 qN//C`

Answer

A

Explanation

`E=Kq[(1)/((1)^2)+(1)/((2)^2)+(1)/((4)^2)+(1)/((8)^2)+......]`

a = 1, r = 1/ 4
`S_n = a/(1-r)=(1/(1-1//4))=4/3`
`E =9 xx10^9 xx4/3 q=12 xx10^9 qN//C`