Attraction of two charged particles

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SUMMARY

The discussion focuses on the dynamics of two charged particles, one with a charge of +1 C and the other with -1 C, placed one meter apart. Using Coulomb's Law, the force is defined as F=k/(r^2)=ma, where r is the distance between the particles. The challenge lies in the changing distance and acceleration, necessitating the formulation of a differential equation to accurately describe their motion. The suggestion to simplify the problem by treating one particle as significantly larger allows for a more manageable analysis of the other particle's trajectory.

PREREQUISITES
  • Coulomb's Law
  • Differential equations
  • Basic mechanics (force, mass, acceleration)
  • Concept of jerk in motion
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omegadir
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I was thinking about this problem today:

You have two nearly identical charged particles, except that one has a charge of +1 C and the other has a charge of -1 C. If you place them at rest one meter apart, how long will it take for them to collide, and what will be their velocities when they do collide?

Using Coulomb's Law, we get F=k/(r^2)=ma. The problem is that r is changing, as well as the acceleration. So, I know there also has to be a jerk term that appears in there somewhere.
Other than that, I'm not sure how to approach this problem.
 
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You have to set up the problem as a differential equation. Notice that a=dv/dt=d^2r/dt^2. The solution is not simple, especially since you have to consider the motion of both particles.

You may want to start off by assuming one of the particles is really large so that you only have to consider the motion of the other particle.
 

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