What is the motion of a particle that fails the velocity selector?

[Lamarr]

in mass spectrometry, velocity selectors are used to select charged particles with a certain velocity.

They use perpendicular electric and magnetic fields. Particles whose velocities equal the ratio of the electric field strength to magnetic flux density are not deflected and are thus "selected"

but what is the motion of a particle which is not selected?

It is neither parabolic nor circular. What is the mathematical equation to describe the particle's path wrt time?

 

[Lamarr]

should i move this to the engineering section instead?

 

[Emilyjoint]

when the ions pass into the magnetic field section they have circular arc paths.
You can imagine the slit being moveable, slide it across and it selects the ions with the appropriate arc... ie speed.
edit
surprised you have not had any other input to your question.

 

[mfb]

Both a parabola and a circle are a good approximation for the path in the velocity selector. If your electric and magnetic fields fill the whole space, you will get the sum of a linear and a circular motion.

Edit: See Philip Woods post for equations, and I can confirm them.

 

[Philip Wood]

Edit: I've changed the notation to bring out the Physics better.

Its path is a cycloid.

Suppose you launch it from the origin, with initial velocity v₀ in the x-direction. Let the magnetic field be B in the z-direction, and the electric field E in the y-direction. Then, unless I've slipped somewhere (quite possible):

$$x=\frac{1}{\omega}\left(v_0 - v_{eq}\right)\:sin{\omega t} + v_{eq}t$$
$$y=\frac{1}{\omega}\left(v_0 - v_{eq}\right)\:\left(cos{\omega t} - 1\right)$$

in which $\omega = \frac{qB}{m}$ ,

and $v_{eq} = \frac{E}{B}$ = speed particle would have to have to be undeflected.

Working can be supplied on thumb-nail if wanted.

 

[Philip Wood]

Lamarr: is this what you wanted?