Question

A charge of `2 C` is at `(-9,1 )` 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

`1.15 xx 10^8 "N"`

Explanation:

The electric force `F` (in `"N"`) between two point charges `q_1` and `q_2` (in `"C"`) is represented by the equation

`F = 1/(4piepsilon_0)(|q_1q_2|)/(r^2)`

where

• `epsilon_0` is a physical constant called the permittivity of free space, equal to `8.8542 xx 10^-12 (C^2)/(N*m^2)`, and

• `r` is the distance (in `"m"`) between the two point charges.

To find the distance between the two charges, we can use the distance formula:

`r = sqrt((1--5)^2 + (-9-2)^2) = color(red)(12.5"m"`

Now that we have all the necessary variables, let's plug them into the equation to find the charge:

`F = 1/(4pi(8.8542 xx 10^-12 (cancel(C^2))/(N*cancel(m^2))))(|(2cancel("C"))(-1cancel("C"))|)/((12.5cancel("m"))^2)`

`= color(blue)(1.15 xx 10^8 "N"`

Thus, the electric force between the two point charges is `1.15 xx 10^8 "N"`, and since the charges are opposite, the force is that of attraction.