An infinite number of charges, each equal to `4mu C` are placed alolng x-axis at x=1m, 2m, 4m, 8 m and so on. Find the total force on a charge of 1C placed at the origin.

Explanation

Here, a charge of 1 C is placed at x=0.
Let, total force on the charge at x=0 due to infinite number of charges of `4 muC` are placed at distance x=1m, x=2m, x=4m, x=0m…… up to `x = infty` be F.

`therefore F=1/(4pi epsilon_(0))[(1 xx 4 xx 10^(-6))/1^(2) +(1 xx 4 xx 10^(-6))/2^(2) +(1 xx 4 xx 10^(-6))/4^(2) + (1 xx 4 xx 10^(-6))/8^(2) +..... + infty]`
`=9 xx 10^(9) xx 4 xx 10^(-6) [1/1^(2) +1/2^(2) +1/4^(2) + 1/8^(2) + ..... +infty]`
`=36 xx 10^(3)[1/(1-1/4]=36 xx 10^(3) xx 4/3]`
`=48 xx 10^(3)` N
Hence, total force acting on the charge at x=0 is `48 xx 10^(3)` N.