(Solved): The diagram at right shows a negative charge with charge Q3 and mass m, that is suspended at ...

The diagram at right shows a negative charge with charge $?Q_3$ and mass $m$, that is suspended at rest. Charge $\#3$ is located a distance $y$ below the ceiling. Two other charges, $Q_1$ and $Q_2$ exert electrostatic forces on charge \#3. $Q_1$ is fastend to the ceiling a distance $x_1$ to the left of the point on the ceiling that is directly above charge \#3. $Q_2$ is at the same height as charge $\#3$ and is fastened to wall that is a distance $x_2$ to the right of charge \#3. 1. What must be the signs of $Q_1$ and $Q_2$ so that charge $\#3$ remains at rest? Both charges are positive $Q_1$ is positive and $Q_2$ is negative $Q_1$ is negative and $Q_2$ is positive Both charges are negative There isn't enough information to determine the signs of the two charges. 2. Let $\begin{array}{l}{F}_{q13}=\text{ the magnitude of the electric force by charge }\#1\text{ on charge }\#3\\ F_{q23}=\text{ the magnitude of the electric force by charge }\#2\text{ on charge }\#3\\ W_{E3}=\text{ the magnitude of the weight by the earth on charge }\#3\text{. }\end{array}$ Write the horizontal and vertical Newton's Second Law equation in terms of $F_{q13},F_{q23}$ and $W_{E3}$ as well as $x_1,x_2$ and $y$. Horizontal Equation: Vertical Equation: 3. Substitute in expressions for the three forces, $F_{q13},F_{q23}$ and $W_{E3}$, then solve the two equations to derive expressions for $Q_1$ and $Q_2$. Both expressions should be in terms of $Q_3,m,x_1,x_2,y$ and the constants $\mathrm{k}$ and $\mathrm{g}$. $\begin{array}{l}{Q}_1=\\ Q_2=\end{array}$