Electrostatic forces between multiple particles

[Phyzwizz]

So I was reading my textbook and it says that we are given a situation where two particles of the same charge are separated by the distance 0.0200m. Another particle of the opposite charge is then placed in between the other two particles, 3/4 the distance mentioned away from one and thus 1/4 away from the other (assuming the radii to be negligible). The book goes on to say that placing this third particle in between the other two does not disrupt the force between these other two particles. This is where I became confused because this would seem to violate the law of conservation of energy. If the force between the original two particles goes unchanged when the third particle is added and yet the two original particles, must also exert another new force on this new particle, where does this extra energy for the extra force needed come from. I would think that the force between the two original particles would have to be reduced in order to be able to have some energy left for the force with the new particle. Whats wrong with my thinking?

 

[MarkoniF]

So I was reading my textbook and it says that we are given a situation where two particles of the same charge are separated by the distance 0.0200m. Another particle of the opposite charge is then placed in between the other two particles, 3/4 the distance mentioned away from one and thus 1/4 away from the other (assuming the radii to be negligible). The book goes on to say that placing this third particle in between the other two does not disrupt the force between these other two particles. This is where I became confused because this would seem to violate the law of conservation of energy. If the force between the original two particles goes unchanged when the third particle is added and yet the two original particles, must also exert another new force on this new particle, where does this extra energy for the extra force needed come from.

They are talking about superposition principle, meaning that fields "overlap" without disrupting each other. To calculate acceleration in that given moment you need to calculate the force between each pair and simply sum up acceleration vectors for each particle.

So first you have only two particles of the same charge and thus they would want to accelerate away from each other. Then you add the third particle of the opposite charge in between and the first two particles would still want to accelerate away from each other just as before, but in the same time they would ALSO want to accelerate towards the third particle. Therefore the end result considering the first two particles would be simply addition of those two acceleration vectors for each of them.

Imagine first two are connected with a compressed spring that wants to expand and push them away. Imagine then they are also connected to the third particle with another spring that is expanded and wants to contract. They are pushed away and pulled in at the same time. That's the point of superposition principle, that these "springs" don't interfere with each other, but their effect simply add up.

I would think that the force between the two original particles would have to be reduced in order to be able to have some energy left for the force with the new particle. Whats wrong with my thinking?

Not force, there would be two forces acting on each particle all the time, and they are two independent vectors. It's acceleration that would be reduced as the net result of those two forces. Acceleration vector you get by vector addition of those two force vectors, where magnitude of the resulting acceleration vector is: a= F/m.

 

[Phyzwizz]

Alright well that makes much more sense, thank you. The book just seems to have worded things in an obfuscatory fashion.