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

Explanation

The figure given below shows two charges `q_(1)=5xx10^(-8)C and q_(2)=-3xx10^(-8)C`. In the given situation, there can be two points on the line joining the two charges at which the electric potential is zero. Let us select points O and O. at which the electric potential is zero.

The electric potential at a point that is at a distance r from a point charge q is given by,
`V=(1)/(4pi epsilon_(0)) (q)/(r )`
From the figure it can be observed that the distances of charged particles `q_(1) and q_(2)` from point O are x and 0.16-x, respectively.
Potential at this point O can be calculated as:
`V=(1)/(4pi epsilon_(0)) [(5xx10^(-8))/(x)-(3xx10^(-8))/(0.16-x)]=0`
`rArr 0.8-5x=3x`
`rArr x=0.1m =10cm`
From the figure it can be observed that the distances of the charged particles `q_(1) and q_(2)` from point O. are y and `0.16+y`, respectively.
The electric potential at the point O. is given by:
`V=(1)/(4pi epsilon_(0))[(5xx10^(-8))/(y)-(3xx10^(-8))/(0.16+y)]=0`
`or, (5xx10^(-8))/(y)=(3xx10^(-8))/(0.16+y)`
`0.8+5y=3y`
`rArr 2y=0.8`
`rArr y=0.4m=40cm`.