Distance of Closest Approach Between Two Charges

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Discussion Overview

The discussion revolves around the concept of the distance of closest approach between two charges, specifically focusing on the dynamics of charged particles under electrostatic repulsion. Participants explore scenarios involving fixed and moving charges, the conditions under which charges stop moving, and the implications of impact parameters on trajectories.

Discussion Character

  • Exploratory
  • Technical explanation
  • Conceptual clarification
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • One participant describes a scenario where a charge ##q_1## is fired towards a fixed charge ##q_0##, questioning how ##q_0## can remain stationary despite the repulsive forces.
  • Another suggests that placing ##q_0## on a non-conducting spherical shell could keep it fixed as ##q_1## approaches.
  • A participant clarifies that the moment when ##q_1## is at rest occurs only briefly before it is repelled back, assuming an impact parameter of zero.
  • Another scenario is introduced where ##q_1## is fixed and a charge ##q_2## is thrown towards it, raising questions about the conditions for the distance of closest approach and the angle of velocity vectors at that point.
  • Participants discuss the conditions under which ##q_1## stops moving, with references to conservation of energy and the balance of forces.
  • There is a discussion about the significance of the impact parameter, with questions about how it affects the trajectory and the conditions for the closest approach.
  • Clarifications are made regarding the mathematical representation of motion, including the relationship between position vectors and their rates of change.
  • One participant expresses confusion about the line of action of forces in relation to the fixed charge, seeking clarification on the geometric interpretation of force lines.

Areas of Agreement / Disagreement

Participants express various viewpoints on how to conceptualize the fixed charge and the dynamics of the moving charge. There is no consensus on the best way to hold ##q_0## fixed or the implications of different impact parameters on the motion of the charges. The discussion remains unresolved with multiple competing views.

Contextual Notes

Participants reference concepts such as conservation of energy, the nature of electrostatic forces, and the geometric interpretation of force lines, but the discussion does not resolve the underlying assumptions or definitions that may affect these interpretations.

  • #61
jbriggs444 said:
they yield equal but opposite torques
Which results in zero torque.
 
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  • #62
gracy said:
Which results in zero torque.
That depends on what you are talking about.

If you are talking about net torque on the system within which both objects are members, then the net torque on that system is zero, yes. That is one way of coming up with the idea that angular momentum must be conserved in a closed system.

If you are talking about the torque on one object or the other then the torque on that object will not be zero [except for the corner case when the "equal but opposite" torques are both zero].
 
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  • #63
jbriggs444 said:
corner case
What's that?
 
  • #64
gracy said:
What's that?
You really do need to use google. Or read books.
 
  • #65
jbriggs444 said:
You really do need to use google.
Shall I type" corner case in torque"?
 
Last edited:
  • #66
jbriggs444 said:
corner case
I think you meant extreme case and that's what I asked when and how that occurs in case of torque ?
jbriggs444 said:
If you are talking about the torque on one object or the other then the torque on that object will not necessarily be zero
I think I have got enough and helpful answers in this thread .Thanks .Not going to ask any further questions on this.
 
  • #67
jbriggs444 said:
The location of ##q_1## is a good choice for a reference point. The fact that it is not moving (in your chosen coordinates) is one reason. Another good reason is because whatever external force holds ##q_1## in place exerts no torque if we choose the location of ##q_1## as the reference point.
In my opinion:
The fact that q1 is stationary, implies that the system of the two particles (charges) is not closed (isolated). There are external forces on q1, keeping it stationary as it interacts with q2. There is a non-zero torque on this system about its center of mass.​

That being said, you can consider the two charges as a system, and as jbriggs444 states, " whatever external force holds ##q_1## in place exerts no torque" {on the system} "if we choose the location of ##q_1## as the reference point."
 
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  • #68
In a pm, gracy asked:
Why are we even taking angular momentum into account{?} I can't see any rotational motion.I mean what will I take in place of r in angular momentum formula L=mvr as r has to be radius of rotation.
​
See Posts #28 and #35. They're gracy's posts.

See what briggs said in post # 34.

Calculate angular momentum as I suggested in post #60.
(I've got to get to my office now. Let briggs continue to help, as he is able.)

(This post has been edited slightly. No relevant content was changed.)
 
Last edited:
  • #69
The gentle advice from Vanadium 50 in #49 seems most appropriate. All that need be said has been said. We are doing gracy no favors by responding.
 
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  • #70
Yes I am done with this thread :smile:
 
  • #71
Same here !
 

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