# A charge of 2 C is at (-3,7) and a charge of -1 C is at ( 5, 2). If both coordinates are in meters, what is the force between the charges?

Dec 23, 2017

The force is $= - 2.02 \cdot {10}^{8} N$

#### Explanation:

The distance between the charges is

$r = \sqrt{{\left(5 - \left(- 3\right)\right)}^{2} + {\left(2 - 7\right)}^{2}} = \sqrt{{8}^{2} + {5}^{2}} = \sqrt{89} m$

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

The force is

$F = {910}^{9} \cdot \frac{2 \cdot - 1}{89} = - 2.02 \cdot {10}^{8} N$