Location of zero net electric force

[gnarkil]

Homework Statement

Particle 0 experiences a repulsion from particle 1 and an attraction toward particle 2. For certain values of d_1 and d_2, the repulsion and attraction should balance each other, resulting in no net force. For what ratio d_1/d_2 is there no net force on particle 0?
Express your answer in terms of any or all of the following variables: k, q_0, q_1, q_2.

Homework Equations

electric force F = kq_1q_2/r^2 where k = 9*10^9, q_1 and q_2 represent charges in coulombs and r is distance in meters between point charges

Fnet = sqrt(F1^2 + F2^2) where F1 is repulsive force and F2 is attractive force

The Attempt at a Solution

Fnet = sqrt(F1^2 + F2^2)
0^2 = F1^2 + F2^2
-F2^2 = F1^2
-[(k*q_2*q_0)/(d_2)^2] = [(k*q_1*q_0)/(d_1)^2]
-(d_1)^2/(d_2)^2 = (k*q_1*q_0)/(k*q_2*2_0)
-d_1/d_2 = sqrt(q_1/q_2)
d1_1/d_2 = -sqrt(q_1/q_2)

correct ratio?

 

[Defennder]

There shouldn't be a negative sign when you're considering distance instead of displacement.

 

[gnarkil]

so aside from the negative sign, the ratio of d1_1/d_2 = sqrt(q_1/q_2) is correct?

 

[LowlyPion]

so aside from the negative sign, the ratio of d1_1/d_2 = sqrt(q_1/q_2) is correct?

Yes.

 

[gnarkil]

okay thanks for the help