# A charge of -2 C is at (6 , -5 ) and a charge of -4 C is at (-3 , -9 ) . If both coordinates are in meters, what is the force between the charges?

Nov 19, 2016

The force between the charges is $0.74 \times {10}^{9}$ Newtons.

#### Explanation:

According to the Coulomb's Law, the magnitude of the electric force exerted by a charge '${q}_{1}$' on another charge '${q}_{2}$' a distance '$r$' away is thus, given by
${F}_{e} = \frac{k | {q}_{1} {q}_{2} |}{r} ^ 2$
Here the value of '$k$' in SI units is
$k = 8.987551787 \times {10}^{9} \frac{N - {m}^{2}}{C} ^ 2$
$k \approx 8.988 \times {10}^{9} \frac{N - {m}^{2}}{C} ^ 2$
Using the given coordinates we can find of the distance between them:
Distance$r = \sqrt{{\left({x}_{2} - {x}_{1}\right)}^{2} + {\left({y}_{2} - {y}_{1}\right)}^{2}}$
Calculating with given values we get ,
$r = \sqrt{97} = 9.84 m$

Substituting all given values in above force equation we get,
${F}_{e} = \left\{8.988 \times {10}^{9} \frac{N - {m}^{2}}{C} ^ 2\right\} \left\{\frac{\left(- 2 C\right) \left(- 4 C\right)}{\sqrt{97} m} ^ 2\right\}$
$\therefore F = 0.74 \times {10}^{9}$ Newtons