# A charge of -3 C is at (-9,1 ) and a charge of -1 C is at ( 2,-5 ). If both coordinates are in meters, what is the force between the charges?

Dec 27, 2015

$1.72 \times {10}^{8} \text{N}$

#### Explanation:

The distance $d$ between the 2 points can be found by completing a triangle with $d$ the hypotenuse.

The $x$ displacement $= 2 - \left(- 9\right) = 11$

The $y$ displacement $= 1 - \left(- 5\right) = 6$

So we can use Pythagoras to get $d$ :

${d}^{2} = {11}^{2} + {6}^{2}$

$\therefore {d}^{2} = 157$

$d = 12.53 \text{m}$

From Coulomb's Law we get:

$F = k . \frac{{q}_{1} {q}_{2}}{d} ^ 2$

$k$ is equal to $9 \times {10}^{9} \text{F/m}$ and is a constant :

$\therefore F = k . \frac{\left(- 3\right) \times \left(- 1\right)}{12.53} ^ 2$

$F = \frac{9 \times {10}^{9} \times 3}{157} = 1.72 \times {10}^{8} \text{N}$