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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`,…………`x=oo` on the x axis, and a charge `-q` is fixed at each of the points `x=2x_0`, `x=4x_0`, `x=6x_0`, …………`x=oo`. Here `x_0` is a positive constant. Take the electric potential at a point due to a 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

A

zero

B

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

C

infinite

D

`(qln(2))/(4piepsilon_(0)x_(0))`

Text Solution

Verified by Experts

The correct Answer is:
D
Potental at origin will be given by
`V=q/(4piepsilon_(0))[1/x_(0)-1/(2x_(0))+1/(3x_(0))-1/4x_(0)+…]`
`=q/(4pi epsilon_(0))(1/x_(0))[1-1/2+1/3-1/4+…]`
`=q/(4piepsilon_(0)x_(0))ln(2)`
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