Time of approach of two oppositely charged particle

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Homework Help Overview

The discussion revolves around the time of approach for two oppositely charged particles, specifically point charges q1 and q2, which are initially at rest and separated by a distance of 1 meter. The problem involves concepts from electrostatics and dynamics, particularly focusing on the forces acting on the charges and their subsequent motion towards each other.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning, Problem interpretation, Assumption checking

Approaches and Questions Raised

  • Participants explore the symmetry of the problem, questioning how the distances of the charges from the center relate to their motion. There are discussions about using calculus to derive the equations of motion and the application of conservation of energy. Some participants express uncertainty about the integration process and the correct setup of variables.

Discussion Status

The discussion is active, with participants providing guidance on setting up equations of motion and considering energy conservation. There is a recognition of the complexity of the differential equations involved, and some participants are attempting to apply trigonometric substitutions to solve integrals. Multiple interpretations of the problem are being explored, particularly regarding the application of Kepler's laws to this scenario.

Contextual Notes

Participants note the importance of correctly defining variables and the potential confusion arising from the signs in the equations. There is also mention of homework constraints, such as the requirement to approach the problem without integrating, which adds to the complexity of the discussion.

  • #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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