CHARGED PARTICLES IN B FIELDS

This is a fascinating study - relevant to charges moving throughout the majority of the universe - the Sun, interstellar space, van Allen belts, Jupiter's vicinity - all over the place!!!!!

( Thanks to the SOHO spacecraft. The "prominence" shown coming from the Sun's surface is composed of charged particles moving in arcs governed by the B fields of the Sun.) For the current weather in space, try www.sec.noaa.gov/

We start our discussion by taking out our mythical (+) charges out of their wire conductor and using simple logic.

F = IlBsinθ

Now if we use the "fact" that each charge has a velocity, v, and I = q Δ t

F = qlBsinθ/ Δ t But v = l / Δ t

so F = qvBsinθ with the RHScrew rule still applying for the force on the charge.

This rule guarantees F is perpendicular to vsinθ so the charge will move in a HELIX - advancing at vcosθ while circling at vsinθ .

RADIUS OF GYRATION

Equating F = qvB to mv² / r gives the radius to be r = mv / qB ,

the radius of gyration.

Note the top term is the MOMENTUM of the charge. This radius must be modified to

r = mvsinθ / qB for the helix.

This property is commonly used by subatomic particle physicists to analyse the debris from the accelerator collisions ( nowadays using state-of-the -art computers ).

APPLICATION ( Chemists love ) - the MASS SPECTROMETER

Many versions now exist of this machine. The first primitive version was the vacuum tube of J. J Thomson who crudely measured mass/charge ratios for ions and electrons thereby showing the very great difference of electrons to atomic ions.

His student, Aston, greatly refined and developed the mass spectrograph into a precision machine capable of resolving individual isotopes.

The machine shown, the Bainbridge variation, uses a mixture of Electric and Magnetic fields to ensure a single velocity stream of ions entering a uniform B field. Separation is by the Radius of Gyration, different ions moving to different radii to be sensed.

How it works

Everything is in a vacuum.

The sample is ionised and injected into the Velocity Filter.

When the ions enter they are subjected by the Electric Force = qE and the Magnetic Force = qvB'. (Notice that the forces are opposite direction, one governed by the direction of E, the other by RHScrew Rule.

If these forces cancel, then the charges are not deflected and they enter the chamber.

Condition for forces cancelling qE = qvB' thus v = E / B' .They all enter at the same speed!!

Here they are analysed according to the gyromagnetic radius, the radius being proportional to the mass as v is common.

INGENIOUS!!!!

Here is more on the Mass Spectrometer