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Can you merge these equations and get acceleration

  1. Jun 11, 2015 #1
    equalizing newton's first law and coulomb's force to get acceleration of the specific charged body.
  2. jcsd
  3. Jun 11, 2015 #2
    I see one equation. And yes, solving for acceleration is as simple as dividing one factor to the other side (note: you are missing the square on your factor 'r').
  4. Jun 11, 2015 #3
    Thanks, and because force changes across distance then acceleration wouldn't be constant so is this a valid formula
  5. Jun 11, 2015 #4
    I trield very hard to solve this equation, i came up with numerical solution, but the exact solution is a bessel x'' = kQq/(x^2 + y^2), a second order differential equation, good luck !
  6. Jun 11, 2015 #5


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  7. Jun 11, 2015 #6
    For sure there are more competent members here to answer this but I don't think it is possible to merge these two equations since ther nature of the two forces involved is different.
  8. Jun 11, 2015 #7
    Answer: kind of.

    The acceleration is valid for the 'initial' acceleration of the charges. The problem is not that the acceleration varies with position (of course, what you have is a differential equation), the problem is that, once the charges are accelerating, Coulomb's force law is no longer valid.
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