# A charge of 2 C is at (-2 , 4 ) and a charge of -1 C is at (7 , 3 ) . If both coordinates are in meters, what is the force between the charges?

Feb 20, 2016

$219.5 \mu N$ attraction

#### Explanation:

First we find the distance between the 2 charges by using the normal Euclidean metric distance formula in ${\mathbb{R}}^{2}$:

d((-2,4);(7,3))=sqrt((-2-7)^2+(4-3)^2)

$= \sqrt{82} m$.

Now we may apply Coulomb's Law in electrostatics to find the magnitude of the electrostatic force between these 2 charges as follows :

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

$= \frac{\left(9 \times {10}^{9}\right) \left(2 \times {10}^{-} 6\right) \left(1 \times {10}^{-} 6\right)}{\sqrt{82}} ^ 2$

$= 219.5 \mu N$.

Since the 2 charges are opposites, they attract each other.