Question

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?

Answer 1

`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

• `k` is the Coulomb's law constant, equal to

`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"`