Question

A charge of `5` `C` is at `(9, 3)` and a charge of `-2` `C` is at `(-2, 7)`. If both coordinates are in meters, what is the force between the charges?

Answer 1

The force between two charges is given by Coulomb's Law: `F=(kq_1q_2)/r^2`. Calculating the distance to be `11.7` `m` and knowing `k=9.0xx10^9` `Nm^2C^-2`, we find `F=9.85xx10^8` `N`

Explanation:

The distance formula for the distance between two points in (2 dimensional) space is:

`d=sqrt((x_2-x_1)^2+(y_2-y_1)^2)`
`=sqrt((-2-9)^2+(7-3)^2)=sqrt137~~11.7` `m`

Using Coulomb's Law we find:

`F=(kq_1q_2)/r^2=(k*5*-3)/11.7^2=(-15k)/137` `N`.

This is the answer in terms of `k`, but we can substitute in the value of the constant to give the final answer in `N`, as shown above.