# A charge of -6 C is at (3, -1 ) and a charge of -1 C is at ( 6,-7 ). If both coordinates are in meters, what is the force between the charges?

Jan 12, 2018

$1.2 \cdot {10}^{9}$ N.

#### Explanation:

First Use The Coordinate Distance Formula to find the distance between the charges.

So, The distance = $\sqrt{{\left(3 - 6\right)}^{2} + {\left(- 1 + 7\right)}^{2}}$ metres = $\sqrt{45}$ metres = $3 \sqrt{5}$ metres.

Now, Simply Use The Coulomb's Formula To Find the Force.

$F = K \frac{{q}_{1} {q}_{2}}{r} ^ 2$ Where K is Coulomb's Law Constant, whose value in SI is $9 \cdot {10}^{9}$ $\frac{N \cdot {m}^{2}}{C} ^ 2$.

$\Rightarrow F = \frac{\left(9 \cdot {10}^{9}\right) \cdot \left(- 6 \cdot - 1\right)}{3 \sqrt{5}} ^ 2$ N = $1.2 \cdot {10}^{9}$ N.