1.

An infinite number of charges , each equal to q , are placed along the x - axis at x = 1, x=2,x=4,x=8 and so on . Thepotential at x = 0 due to this set of charges is

Answer»

`(4Q)/(2piepsilon_(0))`
`2Q//4piepsilon_(0)`
`(q)/(2piepsilon_(0))`
`(2q)/(piepsilon_(0))`

SOLUTION :
Potential at x=0 , due to the above set of charges is
`V=(1)/(4piepsilon_(0))[(q)/(1)+(q)/(2)+(q)/(4)+(q)/(8)+........]`
`=(q)/(4piepsilon_(0))[1+(1)/(2)+(1)/(2^(2))+(1)/(2^(3))+..........]`
`=(q)/(4piepsilon_(0))[(1)/(1-(1)/(2))]=(2q)/(4piepsilon_(0))`


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