# A charge of 5  C is at (9, 3) and a charge of -2  C is at (-2, 7) . If both coordinates are in meters, what is the force between the charges?

Mar 5, 2016

The force between two charges is given by Coulomb's Law: $F = \frac{k {q}_{1} {q}_{2}}{r} ^ 2$. Calculating the distance to be $11.7$ $m$ and knowing $k = 9.0 \times {10}^{9}$ $N {m}^{2} {C}^{-} 2$, we find $F = 9.85 \times {10}^{8}$ $N$

#### Explanation:

The distance formula for the distance between two points in (2 dimensional) space is:

$d = \sqrt{{\left({x}_{2} - {x}_{1}\right)}^{2} + {\left({y}_{2} - {y}_{1}\right)}^{2}}$
$= \sqrt{{\left(- 2 - 9\right)}^{2} + {\left(7 - 3\right)}^{2}} = \sqrt{137} \approx 11.7$ $m$

Using Coulomb's Law we find:

$F = \frac{k {q}_{1} {q}_{2}}{r} ^ 2 = \frac{k \cdot 5 \cdot - 3}{11.7} ^ 2 = \frac{- 15 k}{137}$ $N$.

This is the answer in terms of $k$, but we can substitute in the value of the constant to give the final answer in $N$, as shown above.