Question

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

Answer 1

Correct Answer - c
`E= 1/(4piepsilon_(0)).[(5xx10^(-9))/((1xx10^(-2))^(2))-(5xx10^(-9))/((2xx10^(-2))^(2))+(5xx10^(-9))/((4xx10^(-2))^(2))-((5xx10^(_9)))/((8xx10^(-2))^(2))+ ....]`
`implies E=(9xx10^(9)xx5xx10^(-9))/(10^(-4))[1-1/((2)^(2))+1/((4)^(2))-1/((8)^(2))+....]`
`implies E= 45 xx 10^(4)[1+(1)/((4)^(2))+(1)/((16)^(2))+...] -45 xx 10^(4)[1/((2)^(2))+1/((8)^(2))+1/((32)^(2))+....]`
`implies E= 45xx10^(4)[1/(1-1/(16))]-(45xx10^(4))/((2)^(2))[1+1/(4^(2))+1/((16)^(2))+....]`
`E= 48xx10^(4)-12xx10^(4)= 36xx10^(4)N//C`