Question

Two charges of `-1 C` and `-3 C` are at points `(-2 ,4,-3 )` and `( -3, 5,-81 )`, respectively. Assuming that both coordinates are in meters, what is the force between the two points?

Answer 1

`4.41 xx 10^6` `"N"`

Explanation:

The electric force `F` between two point charges `q_1` and `q_2` separated by a distance `r` is given by 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)`

To find the distance between the two objects, we simply find the distance between the two coordinate points by

`r = sqrt((x_2-x_1)^2 + (y_2-y_1)^2 + (z_2-z_1)^2)`

`= sqrt((-3"m"--2"m")^2 + (5"m"-4"m")^2 + (-81"m"--3"m")^2)`

`= color(red)(78.2` `color(red)("m"`

Since we have all our known variables, let's plug them in to the equation

`F = (8.988 xx 10^9 ("N"·cancel("m"^2))/(cancel("C"^2)))((|(-1cancel("C"))(-3cancel("C"))|)/(color(red)(78.2)cancel(color(red)("m")))^2)`

`= color(blue)(4.41 xx 10^6` `color(blue)("N"`