Time of approach of two oppositely charged particle

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SUMMARY

The discussion revolves around calculating the time of collision between two point charges, q1=1μC and q2=-1μC, each with a mass of 1g, initially 1 meter apart. The participants utilize Newton's laws and conservation of energy to derive the motion equations, ultimately leading to the conclusion that the time of collision is approximately 0.74 seconds. The conversation highlights the importance of using the reduced mass method and Kepler's laws to simplify the problem of two bodies accelerating towards each other due to electric forces.

PREREQUISITES
  • Understanding of Newton's laws of motion
  • Familiarity with Coulomb's law and electric forces
  • Knowledge of differential equations and calculus
  • Concept of conservation of energy in physics
NEXT STEPS
  • Study the reduced mass concept in two-body problems
  • Learn about Kepler's laws and their application to non-gravitational forces
  • Explore advanced integration techniques for solving differential equations
  • Investigate the implications of electric fields as central forces
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Physics students, educators, and anyone interested in classical mechanics and electrostatics, particularly those tackling problems involving forces between charged particles.

  • #61
The trick of applying Kepler's third law is in assuming that motion is elliptic, but the ellipse is "stretched" very severely. Taking this to the limit, it is quite obvious that the time to collision is half the period in elliptic motion. What remains is a reformulation of the law for charged particles.
 
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  • #63
ehild said:
Yes.


Yes. Note that the force is interaction between the real particles. The force the imaginary particle "feels" is equal to that force of interaction, but as if it was exerted by a centre of force in the origin.


If the force of interaction acts along the line connecting the real particles, then it is also towards to or away from the CM of the two-body system.
The imaginary particle also feels central force, acting along the line connecting the particle and the centre (origin)

ehild

Thank You ehild. You helped me a lot.
 
  • #64
You are welcome:smile:

ehild
 

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