# Coulomb's law and vectors

## Main Question or Discussion Point

To find the magnitude of a force between two charges is very simple, but to get the direction of the force seems a little strange to me. The signs of the charges aren't included anywhere in the law, so does this mean that I literally have to think "the signs are opposite, therefore I will multiply the vector by -1 (or leave it positive, depending on my reference coordinates)"? This seems a little bit cumbersome and forced to me, and apparently not derived anywhere in the mathematics of it. Am I going about doing this the right way?

I'm quite accustomed with vectors (vector calculus and linear algebra background), but very new to e&m. Any help would be much appreciated.

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Tide
Homework Helper
The signs are included in Coulomb's law.

"The signs of the charges are not included anywhere in the law". Hmmmmmmmmmmm.
I have a good book with an equation that should help you out.

F= C q1 q2 / r12^2 * (r12)/r12

Where the bolds are vectors, the regular font is scalar
and r12 =r1-r2
where r1 is the location of the q1 and
r2 is the location of q2

If I'm not too clear, I'll fix it up some more

robphy
Homework Helper
Gold Member
The "force on q1 due to q2" is (in agreement with sinyud)
$$\vec F_{on\ q_1\ due\ to\ q_2} = k\frac{q_1 q_2}{r_{12}{}^2} \hat r_{12}$$
where $\hat r_{12}$ is the unit vector at the target charge $q_1$ pointing away from the source charge $q_2$ and
$r_{12}$ is the distance to the target charge $q_1$ from the source charge $q_2$.

If the product $q_1q_2$ is positive (so they have like signs), then,
since $\hat r_{12}$ points away from $q_2$, it follows that$\vec F_{on\ q_1\ due\ to\ q_2}$ points away from $q_2$.
"$q_1$ is repelled by $q_2$."

If the product $q_1q_2$ is negative (so they have unlike signs), then,
since $\hat r_{12}$ points away from $q_2$, it follows that $\vec F_{on\ q_1\ due\ to\ q_2}$ points towards $q_2$.
"$q_1$ is attracted to $q_2$."

Ahh, thanks guys. For some reason I was attaching the unit vector to the equation for the magnitude of the force, which obviously removes the signs from the charges. Major brain fart.

Thanks again.