Two charges `3xx10^-8C and -2xx10^-8C` are located 15 cm apart. At what point on the line joining the two charges is the electrical potential zero? Take the potential at infinity to be zero.

Explanation

`q_(1)=3xx10^(-6)C`
`q_(2)=-2xx10^(-6)C`
r=15 cm 5 cm= Distance between the two charges
`r=15xx10^(-6)C`
Let C is a point at distance x from `q_(1)` where electric potential is zero.
Let `V_(1)` = Electric potential at C due to `q_(1)`
`V_(2)`= Electric potential at C due to `q_(2)`.

and `BC=r-x=15-x`
According to question
`V_(1)+V_(2)=0`
`rArr (1)/(4pi epsi_(0)x)(q_(1))/(x)+(1)/(4pi epsi_(0)) -(q_(2))/((r-x))=0`
`rArr (1)/(4pi epsi_(0)) (q_(1))/(x)=-(1)/(4pi epsi_(0)-(q_(2))/((r-x))`
`rArr (3xx10^(-6))/(x)=(-2xx10^(-6))/((15-x))`
`(3)/(x)=(2)/((15-x))`
`rArr (3)/(x)=(2)/((15-x))`
`rArr 45-3x=2x`
`5x=45`
`rArr x=(45)/(5)=9 cm`
So potential will be zero at at the distance of 9 cm from charge `3xx10^(-6)C`.