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An infinite number of charges, each of c...

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

A

9000 N

B

12000 N

C

24000 N

D

36000 N

Text Solution

Verified by Experts

The correct Answer is:
B
The schematic diagram of distribution of charges on x-axis is shown in figure below:

Total force acting on 1 C charge is given by
`F = (1)/( 4pi epsilon_(0) ) [ (1 xx 1 xx 10^(-6) )/( (1)^2) + (1 xx 1 xx 10^(-6) ) /( (2)^2) + (1xx 1 xx 10^(-6) )/( (4)^2) + (1 xx 1 xx 10^(-6) )/( (8)^2) + .... oo]`
`= (10^(-6) )/( 4pi epsilon_(0) ) ( (1)/(1) + (1)/(4) + (1) /(16) + (1)/(64) + ...oo)`
`= 9 xx 10^(9) xx 10^(-6) ( (1)/(1- (1)/(4) ) )`
`= 9 xx 10^(9) xx 10^(-6) xx (4)/(3) = 9 xx 10^(3) xx (4)/(3) = 12000`N
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