A charge `q_(1) = 1 mu C ` is at a distance 10 cm from another charge `q_(2) = 2 mu C ` . At what point on the line joining the two charges is the electric field strength is zero ?

Explanation

Let electric field be zero at point P which is at a distance x from charge `q_1` , so field at P due to `q_1`

Field at P due to `q_(2)`
i.e., `E_(2) = k "" (q_(2))/((0.1 - x)^(2))`
Now , `|E_(1)| = |E_(2)|`
`k"" (q_(1))/(x^2) = k"" (q_(2))/((0.1 -x)^2)`
`implies (10^(-6))/(x^(2)) = (2 xx 10^(-6))/((0.1 - x)^(2))`
`2x^(2) = (0.1 - x)^(2)`
`implies sqrt2x = 0.1 - x implies 0.1 = (1 + sqrt2) x`
`implies x = (0.1)/(1 + sqrt2) implies x = 0.041`
`therefore` The point is at 0.041 m from charge `q_(1)`