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An assembly of charges +q, -q , +q, -q...

An assembly of charges `+q, -q , +q, -q…..` are at positions `x = 1 m, 2 m, 4 m, 8 m, `…. And so on from origin. What is the potential at `x = 0`, due to these charges ?

A

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

B

`-(q)/(6piepsilon_(0))`

C

`(q)/(6piepsilon_(0))`

D

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

Text Solution

Verified by Experts

`V_(+)=(q)/(4piepsilon_(0)(1))+(q)/(4piepsilon_(0)(4))+(q)/(4piepsilon_(0)(16))+.......`
`(q)/(4piepsilon_(0))(1+(1)/(4)+(1)/(16)+oo)=(q)/(4piepsilon_(0))(1)/(1-(1//4))=(q)/(3piepsilon_(0))`
`V_(-)=(-q)/(4piepsilon_(0)(2))-(q)/(4piepsilon_(0)(8))-(q)/(4piepsilon_(0)(32))-..........`
`=(-q)/(2piepsilon_(0))(1+(1)/(4)+(1)/(16)+......)=(-q)/(6piepsilon_(0))`
`V_("net")=(q)/(3piepsilon_(0))-(q)/(6piepsilon_(0))=(q)/(6piepsilon_(0))`
`:. (C )`
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