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An infinite number of charges each equal...

An infinite number of charges each equal to q are placed along X-axis at `x=1, x=2, x=3,x=4,x=8` and soon. Find the the electric field at the point `x=0` due to this set up of charges.

Text Solution

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At the point x=0, the electric field due to all charges are in the same negative X-direction and hence get added up, i.,e
`E=(1)/(4pi epsi_(0))=[(q)/((1)^(2))+(q)/((2)^(2))+(q)/((4)^(2))+(q)/((8)^(2))+....]`
`=(q)/(4pi epsi_(0))[(1)/(1)+(1)/(4)+(1)/(16)+(1)/(64)+.....]`
`=(q)/(4pi epsi_(0))[ (1)/(1-(1)/(4))]=(q)/(3 pi epsi_(0))` (along negatvie X-axist
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