1. **State the problem:** We have three charges: two charges $Q=6.40\ \mu C$ at points $(0,0)$ and $(0,L)$, and one charge $q=3.00\ \mu C$ at point $(2L,0)$. We need to find the x-component of the force on charge $q$ due to the other two charges when $L=9.50\ \text{cm} = 0.095\ \text{m}$. 2. **Relevant formula:** The force between two point charges is given by Coulomb's law: $$F = k_e \frac{|q_1 q_2|}{r^2}$$ where $k_e = 8.99 \times 10^9\ \text{N m}^2/\text{C}^2$, $q_1$ and $q_2$ are the charges, and $r$ is the distance between them. 3. **Calculate forces from each charge on $q$:** - Force from charge at $(0,0)$ on $q$ at $(2L,0)$: Distance $r_1 = 2L = 2 \times 0.095 = 0.19\ \text{m}$. Force magnitude: $$F_1 = k_e \frac{|Q q|}{r_1^2} = 8.99 \times 10^9 \times \frac{6.40 \times 10^{-6} \times 3.00 \times 10^{-6}}{(0.19)^2}$$ $$= 8.99 \times 10^9 \times \frac{19.2 \times 10^{-12}}{0.0361} = 8.99 \times 10^9 \times 5.32 \times 10^{-10} = 4.78\ \text{N}$$ Direction: along the x-axis from $(0,0)$ to $(2L,0)$, so force on $q$ is repulsive and points in positive x-direction. - Force from charge at $(0,L)$ on $q$ at $(2L,0)$: Distance: $$r_2 = \sqrt{(2L - 0)^2 + (0 - L)^2} = \sqrt{(2L)^2 + L^2} = L\sqrt{5} = 0.095 \times \sqrt{5} = 0.212\ \text{m}$$ Force magnitude: $$F_2 = k_e \frac{|Q q|}{r_2^2} = 8.99 \times 10^9 \times \frac{6.40 \times 10^{-6} \times 3.00 \times 10^{-6}}{(0.212)^2}$$ $$= 8.99 \times 10^9 \times \frac{19.2 \times 10^{-12}}{0.0449} = 8.99 \times 10^9 \times 4.28 \times 10^{-10} = 3.85\ \text{N}$$ Direction: vector from $(0,L)$ to $(2L,0)$ is $(2L, -L)$. Unit vector: $$\hat{r}_2 = \frac{(2L, -L)}{r_2} = \left(\frac{2L}{r_2}, \frac{-L}{r_2}\right) = \left(\frac{2}{\sqrt{5}}, \frac{-1}{\sqrt{5}}\right)$$ So x-component of $F_2$: $$F_{2x} = F_2 \times \frac{2}{\sqrt{5}} = 3.85 \times \frac{2}{2.236} = 3.85 \times 0.894 = 3.44\ \text{N}$$ 4. **Calculate total x-component of force on $q$:** $$F_x = F_1 + F_{2x} = 4.78 + 3.44 = 8.22\ \text{N}$$ 5. **Final answer:** The x-component of the force exerted on charge $q$ by the other two charges is $$\boxed{8.22\ \text{N}}$$