# Two charges of  -1 C  and  5 C  are at points  (1,0,3 )  and  ( -3, 5,-81 ), respectively. Assuming that both coordinates are in meters, what is the force between the two points?

Jan 5, 2018

The force is $= - 6.3 \cdot {10}^{6} N$

#### Explanation:

The force between $2$ charges ${q}_{1}$ and ${q}_{2}$ is

$F = k \frac{{q}_{1} \cdot {q}_{2}}{r} ^ 2$

Where $r$ is the distance between the charges.

And the constant $k = 9 \cdot {10}^{9} N {m}^{2} {C}^{-} 2$

The charge ${q}_{1} = - 1 C$

The charge ${q}_{2} = 5 C$

The distance is

$r = \sqrt{{\left(- 3 - 1\right)}^{2} + {\left(5 - 0\right)}^{2} + {\left(- 81 - 3\right)}^{2}} = \sqrt{16 + 25 + 7056}$

$= \sqrt{7097}$

Therefore,

The force is $= 9 \cdot {10}^{9} \cdot \frac{\left(- 1\right) \cdot \left(5\right)}{7097} = - 0.0063 \cdot {10}^{9} = - {6.310}^{6} N$