Test charge velocity in Coulomb's Law

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Discussion Overview

The discussion revolves around the implications of the velocity of a test charge in the context of Coulomb's Law, particularly in electrostatics where the source charge is considered fixed. Participants explore how the law accommodates the motion of the test charge and the role of time in the force calculation.

Discussion Character

  • Technical explanation, Conceptual clarification, Debate/contested

Main Points Raised

  • Some participants assert that the force on a test charge Q due to a source charge q depends on their velocities, with the source charge at rest leading to a static electric field.
  • Others question why time does not appear in Coulomb's Law if the force is time-varying, seeking clarification on how the law applies to the motion of the test charge.
  • One participant emphasizes that the force is a function of position rather than time, suggesting that measurements of force are consistent regardless of the timing of those measurements.

Areas of Agreement / Disagreement

Participants express differing views on the role of time in Coulomb's Law and the implications of the test charge's motion, indicating that the discussion remains unresolved.

Contextual Notes

The discussion highlights limitations in understanding how time factors into the application of Coulomb's Law, particularly regarding the static nature of the source charge and the dynamic behavior of the test charge.

akhila_k
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The force on a test charge Q due to source charge q, depends on both their velocities in addition to several other quantities. For electrostatics, the source charge is at rest (its velocity is zero) but the test charge may be moving. Then how does Coulomb's Law accommodate for this velocity of the test charge?
 
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akhila_k said:
The force on a test charge Q due to source charge q, depends on both their velocities in addition to several other quantities. For electrostatics, the source charge is at rest (its velocity is zero) but the test charge may be moving. Then how does Coulomb's Law accommodate for this velocity of the test charge?

The source charge is not just at rest, but fixed. This leads to a static (i.e. constant in time) electric field and no magnetic field associated with the source charge. The test charge is then subject to an electrostatic force only, given by Coulomb's law. This force will change over time as the test charge moves.
 
If the force is time varying, why doesn't time parameter appear in Coulomb's law? Or Coulomb's law give the force at what time point in test charge's motion?
 
akhila_k said:
If the force is time varying, why doesn't time parameter appear in Coulomb's law? Or Coulomb's law give the force at what time point in test charge's motion?
The force is a function of position, not time. If you measure the force at point A, move the charge to point B, bring it back to A some time later and remeasure, the force on the charge will have the value that you measured earlier.
 

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