Question

why when solving the problem, A charge Q1=+1.2uC is located at the origin of an (x,y) coordinate system; a second charge Q2=-0.60uC is located at (1.20m, 0.50m) and the third charge Q3=+0.20uC is located at (1.20m, 0) What is the force on Q2 due to the other two charges? The strategy for solving in my textbook says let the distance between charges 1 and 2 be r12 and the distance between charges 2 and 3 be r23, why is that and where did these 12 and 23 come from, I understand r squared is on the bottom for the fraction of coulombs law but what did they do to get 12 and 23 on the bottom?

Answer 1

The notation that has r with a subscript of (12) or (23) means that it is the distance from object/point 1 to 2. In your case, it is the distance from Q1 and Q2, and likewise Q2 and Q3. I hope that was helpful :)

Answer 2

I agree with henryli78 .

It helps you keep things organized. You have multiple distances and you want to refer to them all with the variable \(r\). You have a few charges that you label with numbers, to keep organized.
Look at the second charge. You call it \(Q_2\). Also, it has an location as a point. You could say that its \(P_2\), or \(\left(x_2,\ y_2\right)\). And all these \(_2\)'s mean your variable refers to that charge.

Now there are multiply \(r\)'s you will be using for distance. You will have to calculate the force of \(Q_1\) on \(Q_2\), and the force of \(Q_3\) on \(Q_2\). You will be using two different distances. You can use the labels to indicate which distance your talking about. Like, \(r_{1,\ 2} \equiv \text{Distance from the first charge to the second charge}\). You can read "1, 2" to mean from the first charge to the second charge. For force, \(F_{1,\ 2}\) might mean "force from 1 onto 2."

It's that, or "force on 1 from 2."

It makes the math more organized and easy to follow.

I'll use Coulomb's law to make my example. It will be the same equation you use.

\[F_{\text{on 2, from 1}}=k\frac{Q_1\ Q_2}{r_{1,2}^2}\]\[F_{\text{on 2, from 3}}=k\frac{Q_2\ Q_3}{r_{3,2}^2}\]

Now you have \(r\)-variables that indicate distances, and you can say \(r_{1,2}\) equals something, and \(r_{3,2}\) equals something else! Different variables, all using \(r\) to indicate distance.