So, the question I have is: "How does a charged particle rotating around it's central axis and moving with a constant velocity (v) behave when it enters a magnetic field?" I know the right hand rules and I know how it behaves when it only moves forward with the velocity v. But what happens when she's both doing rotational and translational motion? How does her path look then? And what happens with its velocity and the force acting upon it?(Drawings would be much appreciated.)

What do you expect "both doing rotational and translational motion" to be? The rotational motion a moving charged object undergoes in a magnetic field is not around its own axis - it is a form of translational motion.

Since the force is linear in v, I suspect that any effect due to the rotation will cancel if it's a rigid body and the field is uniform, thus the COM motion would dictate the force. For every charge element giving you one force, there will be an element opposite it giving the same force in the opposite direction. So it seems to me that the rotation only comes into play if the object can deform or the field isn't uniform so the different parts are sampling different fields.

What do you expect "both doing rotational and translational motion" to be? The rotational motion a moving charged object undergoes in a magnetic field is not around its own axis - it is a form of translational motion.

 

Both rotational and translational motion before it goes within the magnetic field since later on, when it enters the field, it changes it's motion... The motion within the magnetic field is what interests me.

 

 

Since the force is linear in v, I suspect that any effect due to the rotation will cancel if it's a rigid body and the field is uniform, thus the COM motion would dictate the force. For every charge element giving you one force, there will be an element opposite it giving the same force in the opposite direction. So it seems to me that the rotation only comes into play if the object can deform or the field isn't uniform so the different parts are sampling different fields.

 

Thank you! That was exactly what I had in mind )

...charged particle rotating around its central axis...

I hope you don't imagine the spin that way, do you?

I hope you don't imagine the spin that way, do you?

Nope. I'm asking for this situation. A perfect rotation aroun its central axis.

Theta pinch, resulting from ions rotating in a vortex, squeezes the ions into the vortex axis, by Lorentz force. The moving ions (a current) create a solenoidal magnetic field through which the ions rotate. See http://en.wikipedia.org/wiki/Pinch_%28plasma_physics%29