An infinite number of charges, each of charge `1 mu C` are placed on the `x`-axis with co-ordinates `x=1,2,4,8….oo` If a charge of `1C` is kept at the origin, then what is the net force action on `1C` charge

Options

A. 9000 N
B. 12000 N
C. 24000 N
D. 36000 N

Answer

B

Explanation

`F_("net")= (1xx1xx10^(-6))/(4piepsilon_0)[1/(1)^2+1/(2)^2+1/(4)^2+1/(8)^2+.....]`
`a =1 , r =1//4`
Sum of infinites series of G.P.
`S_n = a/(1-r)`
`a rarr1^(st) ` term , `r rarr` common ratio
`:.F_("net")=10^(-6) xx 9 xx10^(9) (1/(1-1//4))`
`=9 xx10^3 xx4 //3 = 12000 N`