Question

1. Two point charges 4 μC and 2 μC are separated by a distance 1 m in air. At what point on the line joining the two charges is the electric field intensity zero?

Answer 1

kq1/r^2 = kq2/(1-r)^2
The k's will cross out, then cross multiply
q2 r^2 = q1 (1-r)^2
Then solve for r (you have a little math to do)

Answer 2

let x be the distance from the 4microC charge
k4/x^2=k2/(1-x)^2
(1-x)^2=x^2 /2
1-2x+x^2=x^2 /2
x^2-4x+2=0

x=(4+-sqrt(16-8))/2= 2+-sqrt2
x=2+-1.41=
x=.59 m from the 4micro charge
check the math.