Two point objects carry positive charges of magnitude 5e and 20e . Separation between the charges is 1 cm. Find the location of points on the line joining the two charges where the electric field intensity is zero.

Explanation

As the two charges are of same polarity thus, electric field will be zero at a point between the two charges . Let a point M be located between the two charges where electric field is zero.

Given : `Q_1=5e=5xx1.6xx10^(-19)` C
`Q_2=20e=20xx1.6xx10^(-19)`C
At M, `E_1=E_2`
`rArr 1/(4piepsilon_0)Q_1/x^2 =1/(4piepsilon_0)Q_2/(0.001-x)^2`
`rArr Q_1/x^2=Q_2/(0.01-x)^2`
`rArr (5xx1.6xx10^(-19))/x^2 =(20xx1.6xx10^(-19))/(0.01-x)^2`
`(0.01-x)^2/x^2=20//5`=4
`(0.01-x)/x=pm2`
`rArr x=+1/300m =+1/3 cm` and `x=-1/100` m =-1 cm
x=-1 cm lies on the left side of charge `Q_1`, but on the left side of `Q_1`, the electric fields due to `Q_1` and `Q_2` will be in the same direction , so the net electric field cannot be zero.
The electric field is zero only at `x=+1/3` cm from charge `Q_1` between the two charges.