Question

A charge of `-2 C` is at `(-2 , 1 )` and a charge of `-1 C` is at `(1 ,-3)`. If both coordinates are in meters, what is the force between the charges?

Answer 1

The force between the charges is given by Coulomb's Law, `F = (kq_1q_2)/r^2` , and when the distance is correctly calculated is found to be `1.08*10^9 N`.

Explanation:

The first step is to find the distance between the two charges:

`d = sqrt((x_2-x_1)^2+(y_2-y_1)^2)`
`d = sqrt((1-(-2))^2+((-3)-1)^2)`
`d = sqrt(3^2+(-4)^2) = sqrt(25) = 5`

So the points are `5 m` apart.

Now use Coloumb's Law. The constant k has the value `9*10^9 (Nm^2)C^-2`.

`F = (kq_1q_2)/r^2` = `(9*10^9*-2*-1)/5^2` = `(2.7*10^10)/25`

`F = 1.08*10^9 N`

This is quite a large force, but it's unsurprising because a coulomb is quite a large amount of electric charge, and because the constant in Coulumb's Law is so large (electrostatic forces are much stronger than gravitational forces, for example).