# How exactly do you find the net force between charges?

1. Feb 5, 2013

### paki123

I was doing some homework problems, and I came across a couple I didn't know. I then realized I must have screwed up my understanding on electrical forces.

For an electrical force, if there are two protons, the force is k*q1*q2/r^2. The direction is in the opposite direction.

<---(+) (+)--->

Right?

What would be the net force there assuming the charge is e? Would it be 0 since they are in the opposite direction and have equal distances?

My question is it possible to have a third electron and still have the net force equal to 0?

2. Feb 5, 2013

### Philip Wood

Yes and Yes! If $\textbf{F}_{i, j}$ means the force that charged particle j exerts on charged particle i, then $\textbf{F}_{i, j}$ = $\textbf{F}_{j, i}$. In other words the forces between the particles are equal and opposite.

For three particles,
the force on particle 1 is $\textbf{F}_{1, 2}$ + $\textbf{F}_{1, 3}$
the force on particle 2 is $\textbf{F}_{2, 3}$ + $\textbf{F}_{2, 1}$
the force on particle 3 is $\textbf{F}_{3, 1}$ + $\textbf{F}_{3, 2}$

So the net force, that is the forces on all three particles added together, is zero, because
$\textbf{F}_{1, 2}$ = $-\textbf{F}_{2, 1}$ and so on.