An infinite number of charges each of magnitude q are placed on x-axis at distance of 1, 2, 4, 8, ..... Meter from the origin respectively. Find intensity of the electric field at origin.

Explanation

Let `q_(1)=q_(2)=q_(3)=q_(4)=.....=q`
`r_(1)=1, r_(2)=2, r_(3)=4, r_(4)=8`, ....
The resultant electric field at origin 'O' is given by
`E=1/(4pi epsi_(0)) q_(1)/r_(1)^(2)+1/(4pi epsi_(0)) q_(2)/r_(2)^(2)+1/(4pi epsi_(0)) q_(3)/r_(3)^(2)+1/(4pi epsi_(0)) q_(4)/r_(4)^(2)+` .....
`implies E=q/(4pi epsi_(0)) [1+1/2^(2)+1/4^(2)+1/8^(2)]`
`=q/(4pi epsi_(0))(1-1/4)^(-1) =4/3 q/(4pi epsi_(0))`
`:. E=q/(3 pi epsi_(0))` towards origin.