Physics
posted by Jim .
A point charge +6.7 uC is placed at the origin, and a second charge –3.6 uC is placed in the X  Y plane at (0.40 m , 0.55 m ). Where should a third charge be placed in the plane so that the net force acting on it is zero?

tanα=0.55/0.4 =1.375.
α=54⁰
The distance between the charges
d = sqrt(0.4²+0.55²) = 0.68 m
The electric field at the disired point is zero =>
k•q₁/0.68+r)²=k•q₂/r²,
0.86r²1.36r0.46=0,
r ={1.36±sqrt(1.85+1.58)}/1.72 = >
r₁=1.867 m , r₂=  0.28 m (extraneous root)
d+r=0.68+1.867=2.547 m
x=2.547•cos54=1.5 m
y=2.547•sin54=2.06 m.