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Infinite number of charges each of magni...

Infinite number of charges each of magnitude `q=1 muC` are located at distances 1 m, 2 m, 4 m, ... from the origin on the X-axis. Find the potential at the origin of the coordinate system.

Text Solution

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The potential at X = 0 due to a set of infinite number of charges placed on the X-axis as shown in the figure.

`V =1/(4pi epsilon_(0))(q/1 + 1/2 + 1/4 + 1/8) + ….infty)`
`=q/(4pi epsilon_(0)) (1 + 1/2 + 1/4 + 1/8 + …..infty)`
`=q/(4pi epsilon_(0))[(1-(1/2)^(infty))/(1-1/2)] = q/(4pi epsilon_(0)) xx (1-0)/(1/2)`
`rArr V = q/(4pi epsilon_(0)) xx 2`
`rArr V = 2(9 xx 10^(9) xx 10^(-6)) = 18 xx 10^(3) V`
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