Question

An infinite number of charges each numerically equal to q and of the same sign are placed along the x-axis at `x = 1, x = 2, x = 4, x = 8` and so on. Find electric potential at `x=0`.

Answer 1

Using superpositon principle, we may write electric potential at the origin `(x = 0)` due to various cahrges as
`V = (1)/(4pi in_(0)) [(q)/(1) + (q)/(2) + (q)/(4) + (q)/(8) + …….]`
`V = (q)/(4pi in_(0)) [ (1)/(1) + (1)/(2) + (1)/(2^(2)) + (1)/(2^(3)) + ......]`
As sum of infinite G.P. serious , `S = (a)/(1 - r)` ,
where a is first term and r is common ration.
`V = (q)/(4pi in_(0)) {(1)/((1-1//2))} = (2q)/(4pi in_(0))`