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

[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?

 

[BvU]

Hello @ahmadphy ,

$\qquad$ !​

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.

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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[ahmadphy]

Hello @ahmadphy ,

$\qquad$ !​

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.

$\$

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]

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?

 

[BvU]

Also when I asked if I can say that dt=dx/v is it always mathematically correct?

Well, $v=0$ requires an exception

 

[BvU]

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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