# Two charges of  -7 C  and  -2 C are positioned on a line at points  -9  and  7 , respectively. What is the net force on a charge of  -3 C at  -2 ?

May 30, 2016

color(green)(F_"net")=2.13*10^9" "N

#### Explanation:

$\text{force between "Q_A " and "Q_B" is} :$

$\textcolor{b l u e}{{F}_{1}} = k \frac{\left(- 7\right) \cdot \left(- 2\right)}{7} ^ 2$

$\textcolor{b l u e}{{F}_{1}} = \frac{14 k}{49}$

$\text{force between "Q_B " and "Q_C" is :}$

$\textcolor{red}{{F}_{2}} = k \cdot \frac{\left(- 2\right) \cdot \left(- 2\right)}{9} ^ 2$

$\textcolor{red}{{F}_{2}} = \frac{4 k}{81}$

$\textcolor{b l u e}{{F}_{1}} \text{ and "color(red)(F_3) " are opposite directions}$

$\textcolor{g r e e n}{{F}_{\text{net}}} = \textcolor{b l u e}{{F}_{1}} - \textcolor{red}{{F}_{2}}$

$\textcolor{g r e e n}{{F}_{\text{net}}} = \frac{14 k}{49} - \frac{4 k}{81}$

$\textcolor{g r e e n}{{F}_{\text{net}}} = \frac{1134 k - 196 k}{3969}$

$\textcolor{g r e e n}{{F}_{\text{net}}} = \frac{938 k}{3969}$

$\textcolor{g r e e n}{{F}_{\text{net}}} = \frac{938 \cdot 9 \cdot {10}^{9}}{3969}$

color(green)(F_"net")=2.13*10^9" "N