# A charge of -3 C is at (4 , -6 ) and a charge of -1 C is at ( 2,-5 ). If both coordinates are in meters, what is the force between the charges?

Dec 24, 2017

THe force is $= 5.4 \cdot {10}^{9} N$

#### Explanation:

The net force is

$F = k \frac{{q}_{1} \cdot {q}_{2}}{r} ^ 2$

The charge ${q}_{1} = - 3 C$

The charge ${q}_{2} = - 1 C$

The distance $r = \sqrt{{\left(2 - 4\right)}^{2} + {\left(- 5 - \left(- 6\right)\right)}^{2}} = \sqrt{5}$

The constant $k = 9 \cdot {10}^{9} N {m}^{2} {C}^{-} 2$

Therefore,

$F = 9 \cdot {10}^{9} \frac{\left(- 3\right) \cdot \left(- 1\right)}{5}$

$= + 5.4 \cdot {10}^{9} N$

The $+$ sign indicates that the force is repulsive.