# Two charges of  -1 C  and  5 C  are at points  (1,-5,3 )  and  ( -3 , 9, 1 ), respectively. Assuming that both coordinates are in meters, what is the force between the two points?

Feb 4, 2016

$F = - 2 , 12264 \cdot {10}^{8} N$

#### Explanation:

$\Delta x = - 3 - 1 = - 4$
$\Delta y = 9 - \left(- 5\right) = 14$
$\Delta z = 1 - 1 = 0$
$r = \sqrt{\Delta} {x}^{2} + \Delta {y}^{2} + \Delta {z}^{2}$
$r = \sqrt{16} + 196 + 0$
$\text{distance between two charges is:}$
$r = \sqrt{212}$
${r}^{2} = 212$
$F = k \cdot \frac{{q}_{1} \cdot {q}_{2}}{r} ^ 2$
$F = 9 \cdot {10}^{9} \frac{- 1 \cdot 5}{212}$
$F = \frac{- 45 \cdot {10}^{9}}{212}$
$F = - 2 , 12264 \cdot {10}^{8} N$