# A charge of -2 C is at (1,4 ) and a charge of -1 C is at (12 ,-5) . If both coordinates are in meters, what is the force between the charges?

Jul 11, 2016

$8.9 \cdot {10}^{7} N$

#### Explanation:

Distance between charges:

$| \vec{r} | = \sqrt{\Delta {x}^{2} + \Delta {y}^{2}} = \sqrt{{11}^{2} + {9}^{2}} = \sqrt{202}$

Using Coulomb's law:

$\vec{F} = \frac{{Q}_{1} {Q}_{2}}{4 \pi {\epsilon}_{0} {r}^{2}} \hat{r}$

The direction of the force is along the line connecting the charges radially and we will have ${F}_{12} = - {F}_{21}$ anyway so the direction is not critical. We will find the magnitude now:

$| \vec{F} | = \frac{1}{4 \pi {\epsilon}_{0}} \frac{\left(- 2\right) \left(- 1\right)}{\sqrt{202}} ^ 2 = \frac{1}{2 \pi {\epsilon}_{0} \left(202\right)} = 8.9 \cdot {10}^{7} N$