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An infinite number of charges , each equ...

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 . The potential at x = 0 due to this set of charges is

A

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

B

`2q//4piepsilon_(0)`

C

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

D

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

Text Solution

Verified by Experts

The correct Answer is:
b

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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