Question

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?

Answer 1

`3.46 xx 10^8` `"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(|q_1q_2|)/(r^2)`

where

• `k` is Coulomb's constant, equal to `8.988xx10^9("N"•"m"^2)/("C"^2)`

• `r` is the distance, in `"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"`