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

Jan 27, 2017

According to Coulumbs Law: $m a t h b f F = \frac{k {Q}_{1} {Q}_{2}}{{\left\mid \setminus m a t h b f {r}_{1} - \setminus m a t h b f {r}_{2} \right\mid}^{2}} m a t h b f {e}_{{r}_{1} - {r}_{2}}$

Coulumb's Constant is k approx 8.99×10^9 Nm^2/${C}^{2}$

The magnitude of the force evaluates as:

| mathbf F |= ( 8.99×10^9 * (-2) * (-1))/(abs(((5),(3)) - ((3),(1)))^2) = 2.2475 * 10^9 N

....with ${\left\mid \setminus m a t h b f {r}_{1} - \setminus m a t h b f {r}_{2} \right\mid}^{2} = 8$.

[The answer may look big but note that a charge of "only" 1C is a lot of charge.]