# A charge of -2 C is at (1,4 ) and a charge of -1 C is at ( -2 , 7) . If both coordinates are in meters, what is the force between the charges?

Dec 29, 2015

${10}^{9} \text{N}$

#### Explanation:

$P = \left(1 , 4\right)$

$Q = \left(- 2 , 7\right)$

Using Pythagoras we can say:

stackrel(rarr)(PQ)=sqrt((1-(-2)^2+(4-7)^2)

$\stackrel{\rightarrow}{P Q} = \sqrt{9 + 9}$

$\stackrel{\rightarrow}{P Q} = \sqrt{18} \text{m}$

Coulomb's Law states:

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

$\therefore F = 9 \times {10}^{9} \frac{\left(- 2 \times - 1\right)}{18}$

$F = \frac{\cancel{9} \times {10}^{9}}{\cancel{9}}$

$F = {10}^{9} \text{N}$