An infinite number of charges, each equal to `Q=10 mu C` are placed along the x-axis at `x=1, 3, 9 …..m`. Calculate the magnitude of electric field at `x=0` if the consecutive charge have opposite signs.

Answer

`(8.1/8)xx10^(4) N//C`

Explanation

`q_(1)=+10 mu C=q_(3)=q_(5)`
`q_(2)=q_(4)=q_(6)=-10 mu C`
`r_(1)=1 m`
`r_(2)=3m`
`r_(3)=9 m= 3^(2) m`
`E_("at "0)=(Kq_(1))/r_(1)^(2)-(Kq_(2))/r_(2)^(2)+(Kq_(3))/r_(3)^(2)-(Kq_(4))/r_(4)^(2)+....`
`=Kq[1/1^(2)-1/3^(2)+1/3^(4)-1/3^(6)+ ....]`
`=(Kq)/(1-1/3^(2))=9/8Kq=9/8xx9xx10^(9)xx1xx10^(-6)`
`=8.1/8xx10^(4) N//C`