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

Net force on charge `1 C` at the origin,
`F = K [ (1C xx 1 muC)/(1^(2)) +(1C xx 1 muC)/(2^(2)) + (1C xx 1 muC)/(4^(2)) +……… oo] N`
`= 9xx10^(9) xx10^(-6) [ 1 + (1)/(4) + (1)/(16) + (1)/(64) + …… oo] N`
In brackett, we have geometrical progression whose sum `= (a)/(1-r)`
`F = 9xx10^(3) [(1)/(1-1//4)] = 9000 xx (4)/(3) = 12000 N`