# A charge of -2 C is at (-2 , 1 ) and a charge of 6 C is at (5, 3) . If both coordinates are in meters, what is the force between the charges?

Dec 23, 2017

The force is $= - {2.0410}^{9} N$

#### Explanation:

The distance between the charges is

$r = \sqrt{{\left(5 - \left(- 2\right)\right)}^{2} + {\left(3 - 1\right)}^{2}} = \sqrt{{7}^{2} + {2}^{2}} = \sqrt{53} m$

The force between the charges is

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

The constant $k = 9 \cdot {10}^{9} N {m}^{2} / {C}^{2}$

The charge ${Q}_{1} = - 2 C$

The charge ${Q}_{2} = 6 C$

The force is

$F = {910}^{9} \cdot \frac{- 2 \cdot 6}{53} = - {2.0410}^{9} N$