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

Jul 11, 2017

$3.46 \times {10}^{8}$ $\text{N}$

#### Explanation:

We're asked to find the magnitude of the electric force ${F}_{e}$ between two point charges, which we'll call ${q}_{1}$ and ${q}_{2}$.

To do this, we can use the equation

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

where

• $k$ is Coulomb's constant, equal to $8.988 \times {10}^{9} \left({\text{N"•"m"^2)/("C}}^{2}\right)$

• $r$ is the distance, in $\text{m}$, between the point charges

This distance is found via the distance formula:

r = sqrt((-4-2)^2 + (-1-(-5))^2) = color(red)(7.21 color(red)("m"

Plugging in known values, we have

F_e = 8.988xx10^9("N"•cancel("m"^2))/(cancel("C"^2))((|(2cancel("C"))(-1cancel("C"))|)/(color(red)(7.21)cancel(color(red)("m"^2))))

= color(blue)(3.46xx10^8 color(blue)("N"