An infinite number of charges each equal to q, are placed along the X-axis at `x = 1, x = 2, x = 4, x = 8`,…….. and so on.
(i) find the electric field at a point `x = 0` due to this set up of charges.
(ii) What will be the electric field if the above setup, the consecutive charges have opposite signs.

Options

A. `(2q)/(3) , 4q`
B. `(2q)/(5) ,(4q)/(5)`
C. `(2q)/(3),(4q)/(5)`
D. `(2q)/(5),(4q)/(7)`

Answer

3

Explanation

`V_(o) = (q)/(4 pi in_(0)) [ 1 - (1)/(2) + (1)/(4) + …oo = (1)/(1 - (-1//2))]`
` = (1)/(4 pi in_(0)) [ (2q)/(3)]`
`E_(0) = (q)/(4 pi in_(0)) [ 1 - (1)/(4) + (1)/(16) - … = (1)/( 1 - (-1//4))]`
`= (1)/(4 pi in_(0)) .(4q)/(5)`