# A charge of 2 C is at (-3 ,7) and a charge of -1 C is at ( -3 ,5 ). If both coordinates are in meters, what is the force between the charges?

Jun 7, 2017

$4.49 \times {10}^{9}$ $\text{N}$

#### Explanation:

We're asked to find the electric force acting between two point charges.

To find the magnitude of the force $F$ (in $\text{N}$) between two point charges, we can use the equation

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

where

$8.988 \times {10}^{9} \left({\text{N" · "m"^2)/("C}}^{2}\right)$

• ${q}_{1}$ and ${q}_{2}$ are the two point charges (in $\text{C}$), in any order

• $r$ is the distance (in $\text{m}$) between the two charges

to find this, we simply find the distance between the two given coordinates:

r = sqrt((-3 - -3)^2 + (7-5)^2) = color(red)(2 color(red)("m"

Plugging in our known values, we have

F = (8.988 xx 10^9 ("N" · cancel("m"^2))/(cancel("C"^2)))(|(2cancel("C"))(-1cancel("C"))|)/((color(red)(2)cancel(color(red)("m")))^2)

= color(blue)(4.49 xx 10^9 color(blue)("N"