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I On the logical-ness of the principle of superposition

  1. Apr 5, 2016 #1
    I am aware that there have been a few posts about this, I read most of them so I just want to confirm that what I've picked up is correct.

    The principle of superposition only applies to forces that depend linearly on some quantity (charge and mass for example), and since we wouldn't know whether or not the force is linear until we do experiments with three charges, there is no way of knowing until that experiment confirms the linearity of the (in this case) electric force with respect to q.

    I haven't really learned much about linearity formally in school, and thanks to how weak American math education is (11th grade now), I had to pick all this up on my own. If the terminology I used or explanation was not satisfactory, please point it out. Thanks friends.
     
  2. jcsd
  3. Apr 5, 2016 #2

    dextercioby

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    I think what you call „superposition principle” could be seen as the mathematical rephrasing to the simple fact that forces are genuine vectors, hence members of a mathematical construct called vector space. The sum of two vectors in this space is then defined to be the total force acting on a massive material point. One then has a different, more important principle which states that forces upon a massive material point act independently, more precisely, let A, B, C be 3 bodies of masses mA, mB and mC. Then the total force exerted by B on A is independent of the presence of C, thing which mathematically reads into the fact that the overall potential energy of this 3-particle system is a sum of 3 functions each depending on 2 variables only.

    So if the Coulomb force were F(q1,q2) = K q_1 ^2 q_2 ^2 / r^4 r, then this would still be subject to the „superposition principle”, even if the dependence on electric charges would no longer be linear.
     
  4. Apr 10, 2016 #3
    Superposition is not a feature of particular forces, is it a feature of the differential equations used to describe whatever is under consideration. If the DEs are linear, solutions will exhibit superposition. If the DEs are nonlinear, solutions will not.
     
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