Circular motion as a result of the Lorentz force

[akansh_karthik_1]

TL;DR Summary

If the lorentz force results in circular motion then how do machines like railguns and MHD drives acheive inear motion? Is this because of the electric field? Does the electric field affect or conteract Circular Motion?

If a charged particle moves with velocity V over a perpendicular margnetid feild B then the particle experiences lorentz force F = q(V x B). This force eventually results in what is called circular motion where the magnetic force becomes centripetal. However if the Lorentz force results in circular motion then how do devices like railguns and MHD drives acheive linear force. I have a hunch that this is because of the electric field in railguns and MHDs which is parallel to the velocity of the particle and perpendicular to the magnetic field, but I am not sure.

 

[BvU]

Google Lorentz force. There is a (vector) $\vec E$ in there !

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Or google linear accelerator

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[akansh_karthik_1]

Google Lorentz force. There is a (vector) $\vec E$ in there !

​

Or google linear accelerator

$\$​

So if there is an electric field and a magnetic field will there not be circular motion? By the way thank you for responding.

 

[BvU]

Correct

 

[akansh_karthik_1]

Correct

And the motion will just be linear(perpendicular to both E and B)?

 

[berkeman]

And the motion will just be linear(perpendicular to both E and B)?

Not necessarily...

 

[akansh_karthik_1]

Why do they move like that?

 

[berkeman]

Did you watch the whole video? After a minute or two of the animation, they change to a lecture discussing the math...

 

[akansh_karthik_1]

Did you watch the whole video? After a minute or two of the animation, they change to a lecture discussing the math...

Sorry I just got to it now. In the video it says that if the motion of the particle is linear then the magnetic and electric force have to cancel each other out. But in this scenario the particle does not experience any acceleration. I did some research and everything seems to point to the Lorentz force not causing linear motion, this is also indicated by the cross product in the formula, but what confuses me is that if Lorentz force cannot cause linear motion then how do devices like railguns accelerate their shells linearly?

 

[berkeman]

if Lorentz force cannot cause linear motion then how do devices like railguns accelerate their shells linearly?

It can cause linear motion/acceleration if there are mechanical constraints on the motion of the metal rod or projectile.

Are you familiar with calculating the motion of a metal rod sitting on top of metal rails as part of a conducting loop?

https://phys.libretexts.org/Bookshe...ectromagnetic_Induction_and_the_Lorentz_Force

 

[renormalize]

how do devices like railguns accelerate their shells linearly?

The velocity $\boldsymbol{v}$ of the electrons in the current $\boldsymbol{I}$ through the projectile, crossed into the magnetic field $\boldsymbol{B}$ around the rails, results in a linear force $\boldsymbol{F}$ on the projectile that's parallel to the direction of the rails:

(from https://en.wikipedia.org/wiki/Railgun)

 

[akansh_karthik_1]

That makes a lot more sense. Thank you everyone!