Coulomb's law three points on a line

[Roodles01]

Homework Statement

Three point charges, q1, q2 and q3 all on x-axis (i.e y=0 and z=0)
+q1 at x = 0
-q2 at dist from origin x = a
+q3 at dist from origin x = -2a
where q1, q2 and q3 are magnitudes of the charges.

Assuming q1 = q2 derive magnitude of q3 in order for there to be zero net force on q1.

Homework Equations

Coulombs law
F₁₂ = (q1 * q2) / (r₁₂)² rhat₁₂

The Attempt at a Solution

attempt 1
in order for there to be no force on q1 then,
-q2(a) = q3(2a)
so
q3 = (-q2*a)/2a = -q2/a

bit too simplistic?

or attempt 2
F₁₂ = 1/4*∏*ε₀ * (q1*q2) / (r₁₂)² rhat₁₂ .
F₁₂ = 1/4*∏*ε₀ * (q1*q2) / (a²) e_x

F₁₃ = 1/4*∏*ε₀ * (q1*q3) / (r₁₃)² * rhat₁₂
F₁₃ = 1/4*∏*ε₀ * (q1*q3) / (-2a²) -e_xResultant
magnitude F₁ = 0 = 1/4*∏*ε₀ * ((q1*q2) / (a²) e_x + (q1*q3) / (-2a²) -e_x

agh, run out of input time, will be back
Am I on the right track?

 

[mfb]

-q2(a) = q3(2a)

What does that mean? Charge as function of distance?

(-q2*a)/2a = -q2/a

That equation cannot be true.

In attempt 2, there are many missing brackets. Apart from that, it looks good.