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An assembly of charge +q, -q, +q, -q,……....

An assembly of charge `+q`, `-q`, `+q`, `-q`,…….are placed at distance `x=1m`, `x=2m`, `x=4m`, `x=8m`,…..,from the origin, in a plane. The potential at `x=0` due to the charges would be

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