Test charge velocity in Coulomb's Law

[akhila_k]

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?

 

[PeroK]

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.

 

[akhila_k]

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?

 

[kuruman]

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.