Question

A charge of `-2 C` is at `(1,4 )` and a charge of `-1 C` is at `(12 ,-5)`. If both coordinates are in meters, what is the force between the charges?

Answer 1

`8.9*10^7N`

Explanation:

Distance between charges:

`|vec(r)| = sqrt(Deltax^2+Deltay^2) = sqrt(11^2+9^2) = sqrt(202)`

Using Coulomb's law:

`vec(F) = (Q_1Q_2)/(4piepsilon_0r^2)hat(r)`

The direction of the force is along the line connecting the charges radially and we will have `F_(12) = -F_(21)` anyway so the direction is not critical. We will find the magnitude now:

`|vec(F)| = 1/(4piepsilon_0)((-2)(-1))/(sqrt(202))^2 = 1/(2piepsilon_0(202)) = 8.9*10^7N`