How exactly do you find the net force between charges?

  1. 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.

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


    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. jcsd
  3. Philip Wood

    Philip Wood 1,180
    Gold Member

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

    For three particles,
    the force on particle 1 is [itex]\textbf{F}_{1, 2}[/itex] + [itex]\textbf{F}_{1, 3}[/itex]
    the force on particle 2 is [itex]\textbf{F}_{2, 3}[/itex] + [itex]\textbf{F}_{2, 1}[/itex]
    the force on particle 3 is [itex]\textbf{F}_{3, 1}[/itex] + [itex]\textbf{F}_{3, 2}[/itex]

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