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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

Text Solution

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Potentia at origin will be given by
`V = (q)/(4pi in_(0)) [(1)/(x_(0)) - (1)/(2x_(0)) + (1)/(3x_(0)) - (1)/(4x_(0)) + ….]`
`=(q)/(4pi in_(0)) (1)/(x_(0)) [1-(1)/(2) = (1)/(3) -(1)/(4) + …]`
`=(q)/(4pi in_(0)x_(0)) ln (2)`
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