Two charge `5xx10^(-8)C ` and `-3xx10^(-8)` C are located 16 cm apart. At what point(s) on the line joining the two charges is the electric potential zero ? Take the potential at infinity to be zero.

Explanation

Here are two possibilities. First possibillty :
Let charge `q_(1) = 5xx10^(-8) ` C and `q_(2) =-3xx10^(-8) ` C are placed at point A and B respectively. AB = 0.16 m

Let electric potential at point P is zero
`:.` Electric potential at Point P
`V = V_(1) +V_(2)`
`O=(kq_(1))/(x) +(kq_(2))/(0.16-x)`
`O = (5xx10^(-8))/(x) -(3xx10^(-8))/(0.16-x) [ because ` Dividing by k]
`:. (3xx10^(-8))/(0.16-x)=(5xx10^(-8))/(x)`
`:. (3)/(0.16-x) =(5)/(x)`
`:. 3x=0.8 -5x`
`:. 8x=0.8`
`:. x = 0.1 `m
`:. ` It is zero from 0.1 m away from `5xx10^(-8) ` C or
It is zero from 0.06 m away from `-3 xx10^(-8) C `
Second possibillity :

`V= V_(1) + V_(2)`
`:. 0 =(kq_(1))/(x) (kq_(2))/(x-16)`
`:. (q_(1))/(x) = (q_(2))/(x-16)`
`:. (5)/(x xx 10^(-2))= (3)/((x-16)xx10^(-2))`
`:. (5)/(x) =(3)/(x-16)`
`:. 5x-80=3x`
`:. 2x=80 `
`:. x = 40 cm`
`:.` 40 cm away from `q_(1)` cahrge or 24 cm away from `q_(2)` charge.