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

An infinite number of charges, each of charge q, are located along the x-axis at x=1, x=2 x=4, x=8 and so on. Find the potential at x=0.

Text Solution

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From, super positon principle, we get electric potential at the origin (x = 0) due to various charges as,
`V = q/(4piepsilon_0)[q/x_1+q/x_2+q/x_3+q/x_4+...]`
`= q/(4piepsilon_0)[1/1+1/2+1/4+1/8+...]`
`= q/(4piepsilon_0)[1/1+1/2+1/2^2+1/2^3+...]`
As sum of infinite geometric progression series
`S = a/(1-r)`
Where a - first term
r- common ratio
`V= q/(4piepsilon_0){1/((1-1/2))}`
`= q/(4piepsilon_0)[1/(1/2)]=(2q)/(4piepsilon_0)`
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