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Motion of charged particles

  • Thread starter BOYLANATOR
  • Start date
  • #1
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Homework Statement


This is a problem I was thinking about which I haven't come across in my course.

Two particles with mass, m, and a positive charge, q, are separated by a distance r0. One particle is unable to move while the other is released and is repelled. Find an equation for the motion of the particle.


Homework Equations


F=q2/cr2

a=F/m

The Attempt at a Solution



The problem I have in working out the acceleration at any time here is that r is a time dependent variable.
Although this seems like a pretty important thing to know how to calculate I end up going around in circles with the maths.
 

Answers and Replies

  • #2
6,054
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This is not a simple problem. Even if we assume that the accelerating particle does not radiate energy (which in reality it would do), we still end up with a differential equation. You can get this equation from conservation of total energy. The resultant equation can be integrated, but it will be a complicated expression, where the distance depends on time implicitly.
 
  • #3
gneill
Mentor
20,793
2,773
You can easily find the velocity at some position r via the change in potential energy that occurs in moving from position ro to new position r. That'll give you some expression:

##v = \sqrt{f(r)}##

where f(r) is a function of r (it's for you so work out!).

Then make v = dr/dt, shuffle to group the appropriate variables and integrate both sides. That'll leave you with an expression of the form t = g(r), for g some function of r (again, for you to work out).

As for finding r in terms of t, that is, r(t), well you might find that solving t = g(r) for r is not trivial. Good luck!
 

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