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A charge +q is fixed at each of the poin...

A charge `+q` is fixed at each of the points `x = x_0, x = 3x_0, x = 5x_0,` and so on, on the x-axis, and a charge `-q` is fixed at each of the points ` x= 2x_0, x = 4x_0, x = 6x_0,` and so on. Here, `x_0` is a positive constant. Take the electric potential at a point due to charge Q at a distance r from it to be `Q//4piepsilon_0r`. Then, the potential at the origin due to the above system of charges is

A

zero

B

infinity

C

`(q)/(8piepsilon_(0)x_(0)ln2)`

D

`(qln2)/(4piepsilon_(0)x_(0))`

Text Solution

Verified by Experts

`V=(q)/(4piepsilon_(0))((1)/(x_(0))-(1)/(2x_(0))+(1)/(3x_(0))-(1)/(4x_(0))+...)=(q)/(4piepsilon_(0)x_(0))(1-(1)/(2)+(1)/(3)-(1)/(4)+...)=(q)/(4piepsilon_(0)x_(0))ln(2)`
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