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?

1 Answer
Jun 7, 2017

4.49 xx 10^9 "N"

Explanation:

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

To find the magnitude of the force F (in "N") between two point charges, we can use the equation

F = k(|q_1q_2|)/(r^2)

where

8.988 xx 10^9 ("N" · "m"^2)/("C"^2)

  • q_1 and q_2 are the two point charges (in "C"), in any order

  • r is the distance (in "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"