Three particles, finding Q of one of them (Coulomb's Law)

[syladelaney]

Homework Statement

"A particle with charge -3.03 nC is at the origin, and a particle with negative charge of magnitude Q is at x = 49.0 cm. A third particle with a positive charge is in equilibrium at x = 20.8 cm. What is Q?"

Homework Equations

I'm fairly certain that Coulomb's Law is the basis of this problem. I'm not entirely sure what all to put in this section, so I'm posting a few derivations of it.

E = F/q
F = k*(qQ/r^2)
E = k*Q/r^2
k = 8.99*10^9

The Attempt at a Solution

k*(-3.03nC)q/(.208m)^2 = k*Q*q/(.490)^2
^here I basically plugged values for the second equation above and set the forces equal to each other.
rearranging the equation and cancelling variables I got...
Q = (-3.03nC)*(.490/.208)^2
And solved to get Q = -16.8, which is evidently not correct.

I'm not sure if I manipulated the formulas wrong, made a mathematical error, or am approaching this with a fundamental misunderstanding. Also, I apologize if my formatting was hard to read. I'm new to the forums.
Thank you so much!

 

[BvU]

Hello syladelaney,

k*Q*q/(.490)^2

What force is this ?

 

[BvU]

which is evidently not correct

Why is that so evident ?

 

[kuruman]

Your fundamental misunderstanding is that you started "manipulating" formulas and set things equal to each other without a strategy. You put the cart before the horse. First state your strategy and then implement it by manipulating formulas and setting things to each other. So what is your strategy here?