Two positive point charges `q_1=16muC` and `q_2=4muC` are separated in vacuum by a distance of `3.0m`. Find the point on the line between the charges where the net electric field is zero.-

Explanation

Between the charges the two field contributions have opposite direction, and the net electric field is zero at a point (say P) where the magnitude of `vec(E)_(1)` and `vec(E)_(2)` are equal.
However, since `(q_(1) gt q_(2))` point P must be closer to `q_(2)`, in order that the field of the smaller charge can balance the field of the larger charge.
AT P, `E_(1) = E_(2)`
or `(1)/(4pi epsilon_(0))(q_(1))/(r_(1)^(2)) = (1)/(4pi epsilon_(0))(q_(2))/(r_(2)^(2))`
`(r_(1))/(r_(2)) = sqrt((q_(1))/(q_(2))) = sqrt((16)/(4)) = 2`
Also, `r_(1) + r_(2) = 3.0 m :. r_(1) = 2m, r_(2) = 1m`
Hence, the point P is at a distance 2m from `q_(1)` and 1m from `q_(2)`.