path of charged particle through magnetic field

i think the answer will come from F = v x B and all that stuff... try:

If you have a dc voltage gradient between parallel plates you will get what is called E cross B motion. The electron will move towards the positive plate but will be curved by the magnetic field so it will move in an arc that eventually takes it back towards the negative plate so it will slow back down and stop, then start moving towards the postive plate again, etc. If there is no field but the particle has some kinetic energy it will move in a curved path, and if the field is strong enough relative to the kinetic energy and the mass to charge ratio the path will be a circle. It turns out that the time required to go around one circular orbit is independent of the kinetic energy, and this is called cyclotron motion with a frequency given by omega = 2 * PI * frequency in hertz = q B / m, with q in coulombs, m in kg, and B in tesla. If you put the particle between two parallel plates as before but instead of dc voltage you apply ac voltate at the cyclotron frequency the particle will absorb energy and as it gains kinetic energy it will spiral outward. In a sector mass spectrometer ions are generated in a source region and then accelerated into the region with a perpendicular magnetic field. At constant accelerating potential all ions have the same kinetic energy but ions with high m/z (mass to charge ratio) will be barely deflected while ions with low m/z will be greatly deflected so where the ions exit the magnetic field region is determined by the m/z. This is one way to do things, but now you need an array detector to get all the signals. Another way is to use a slit in front of one detector and to scan the magnetic field so ions of progressively higher m/z (assuming the magnetic field is being increased) are deflected into the slit.

Anyway, that's a start. The force on a particle moving with velocity v perpendicular to a magnetic field is qvB (charge times velocity times magnetic field strength) in a direction perpendicular to the instantaneous direction of the ion's motion. That, plus ke=1/2 * m * v

• v are about all you need to derive the equations of motion. Motion of an ion in the direction of the magnetic field is not affected by the field.

-- Regards, Carl Ijames carl dott ijames aat verizon dott net (remove nospm or make the obvious changes before replying)

wrote in message news: snipped-for-privacy@a35g2000prf.googlegroups.com...

Its not that difficult

The force on an charge is F = q*(E + v x B)

But Newton tell sus F = ma

so

ma = q*(E + v x B)

this is a system of differential equations which you can solve given m, q, E, and B with the initial conditions

If, say, E is 0 and B is constant with q = m then

a = v x B

if r = (x,y,z) is the position, then

v = r' a = r''

and, say,

B =

then

a =

==>

x'' = 0 y'' = z' z'' = -y'

or

x = at + b, y'' = -y z'' = z

=>

x = at + b y = c*cos(t) + d*sin(t) + e z = f*cos(t) + g*sin(t) + h

which you can solve given the initial conditions. If d = f = 0 then it is "spirals if there is an initial veleocity in the x direction(a != 0).

You also know that E = -grad(V) so if V is not constant then you can compute the force given the equation above for general V and B.

Its not hard as everything you want to know is contained in ma = q*(E + v x B)

even if E and B are changing with time you can solve the equation(numerically of course) but in general you'll probably also need maxwells equations because E and B are related.

Jon

snipped-for-privacy@gmail.com snipped-for-privacy@gmail.com posted to sci.electronics.design:

The first fundamental idea is that you are dealing with a mass spectrometer type apparatus. They are specifically designed to work very specifically on mass/charge ratio. Specifically the magnetic field area is isolated from the electric field area. That is quite a tricky bit of shielding BTW. the path is necessarily curved, but not necessarily a spiral nor any epicycle. The B fields are generally setup up to preclude spiral or epicyclical paths. If you have an object that is producing spiral paths, perhaps you have a magnetron or possibly a gyrotron.

Also possibly Special Relativity if the electrons are fairly high energy