I The effect of a field on a particle depends on the particle velocity?

AI Thread Summary
The discussion centers on how a vector field affects a particle's momentum, questioning whether this effect depends on the particle's speed and the time interval it experiences the force. It acknowledges that the Lorentz force is a relevant example, particularly for charged particles in magnetic fields. The relationship dt = dx/v is confirmed as a definition of velocity, but the force itself does not depend on the time interval. The conversation also touches on D'Alembert's principle and the concept of inertial force related to kinetic energy, suggesting that the path of a particle can be analyzed from both moving and rest perspectives. Overall, the complexities of these principles and their mathematical validity are explored.
ahmadphy
Assume there is a force (vector field) on the space .....does the effect of this field on the particle(the change of momentum) at some position depend on the speed at that position? And is it related to the time interval dt the particle experiences this force ? Can i say dt=dx/v? And is that related to the inertial force of the particle due its kinetic energy?
 
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Hello @ahmadphy ,
:welcome: ## \qquad## !​
ahmadphy said:
Assume there is a force (vector field) on the space .....does the effect of this field on the particle(the change of momentum) at some position depend on the speed at that position?
That is possible, yes. Example: charged particle in a magnetic field. Google Lorentz force.

ahmadphy said:
And is it related to the time interval dt the particle experiences this force ? Can i say dt=dx/v? And is that related to the inertial force of the particle due its kinetic energy?
The force itself does not depend on ##{\rm d} t##.
You can say ##{\rm d }t={\rm d} x/v## because that's the definition of ##v##.
[ edit ] mathematicians may frown on this...I don't know what 'the inertial force of the particle' means.

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BvU said:
Hello @ahmadphy ,
:welcome: ## \qquad## !​

That is possible, yes. Example: charged particle in a magnetic field. Google Lorentz force.The force itself does not depend on ##{\rm d} t##.
You can say ##{\rm d }t={\rm d} x/v## because that's the definition of ##v##.
[ edit ] mathematicians may frown on this...I don't know what 'the inertial force of the particle' means.

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Thank you...I know lorentz force...what I want from the question is to understand d'alembert's principle and what I meant by inertial force of the particle due to its kinetic energy is that when a force acts on a moving body it will follow some path I can have the same path if I assumed the particle is at rest and transformed the kinetic energy to force then apply the same force as the situation when it was moving
 
ahmadphy said:
Thank you...I know lorentz force...what I want from the question is to understand d'alembert's principle and what I meant by inertial force of the particle due to its kinetic energy is that when a force acts on a moving body it will follow some path I can have the same path if I assumed the particle is at rest and transformed the kinetic energy to force then apply the same force as the situation when it was moving
Also when I asked if I can say that dt=dx/v is it always mathematically correct?
 
ahmadphy said:
Also when I asked if I can say that dt=dx/v is it always mathematically correct?
Well, ##v=0## requires an exception :wink:
 
ahmadphy said:
Thank you...I know lorentz force...what I want from the question is to understand d'alembert's principle and what I meant by inertial force of the particle due to its kinetic energy is that when a force acts on a moving body it will follow some path I can have the same path if I assumed the particle is at rest and transformed the kinetic energy to force then apply the same force as the situation when it was moving
I really still don't understand... Do you have a reference or an example?

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