How to solve for unknown charge position

samedi 31 août 2013

1. The problem statement, all variables and given/known data

2. Relevant equations

Coulomb's Law

3. The attempt at a solution

Here are 2 different possibilities I drew that I think will have the x component vectors and y component vectors cancel out, but I think there may be some other positions as well.

##\textbf{F}_x = k_e [\frac{(1.0 \textrm{ uC} \cdot q3) \cdot cos(\theta_1) \cdot \hat{r}_{13}}{{r_1}^2} + \frac{(-3.0 \textrm{ uC} \cdot q3) \cdot cos(\theta_2) \cdot \hat{r}_{23}}{{r_2}^2}]##

##\textbf{F}_y = k_e [\frac{(1.0 \textrm{ uC} \cdot q3) \cdot sin(\theta_1) \cdot \hat{r}_{13}}{{r_1}^2} + \frac{(-3.0 \textrm{ uC} \cdot q3) \cdot sin(\theta_2) \cdot \hat{r}_{23}}{{r_2}^2}]##

But there are so many unknowns and I only have one equation (Coulomb's) so I'm not sure what to do from here.