Download Charged Particles in Magnetic Fields

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Charged Particles in Magnetic Fields and Mass Spectrometers
Introduction
Suppose a particle with charge q and mass m moves with velocity vector v. If a force F acts in the same
direction as the velocity v then the particle continues to move in the same direction, but it speeds up. This is
what an electric field can do to charged particles. We can describe it a bit differently by saying the electrical
force (associated with the electric field E) does work on the charged particle--which can change the particle's
kinetic energy.
Consider now the same particle subject to a magnetic force. Such a force always acts at right angles to the
velocity vector v. Since there is no component of this force acting in the direction of the displacement, it does
zero work on the particle. Thus it cannot change the particle's kinetic energy. Figure #1 shows the motion of
an electron in a uniform magnetic field B directed down into this sheet. Use the right hand rule to verify that
the magnetic force F points down when the electron is at point P. Note as it moves from position P to Q the
direction of its velocity vector changes. Magnetic forces change the direction of motion, but not the speed. The
result is the particle moves in a circle of radius r. Note the magnetic force provides the centripetal force that
maintains such uniform circular motion. Applying F = m a, recalling centripetal acceleration is v2 /r, leads to
q v B = m v2 /r and r = mv /q B, (equation #1). Solving for charge to mass ratio, q / m = v / r B (equation #2).
Figure #1
The Path of an Electron in a
Uniform Magnetic Field
Figure #2-- The mass spectrometer
Table #1
is an important tool for doing
chemical analyzes. It distinguishes
particles of interest by the fact that,
if their velocities are the same,
different charge to mass (q / m)
ratios lead to different circular path
radii r, according to equation #1.
Note that the position x (distance
between entry point and where
particle is detected on screen or
photographic plate) = 2 r.
Objective:
'To better understand motion of charged particles in magnetic fields and the operation of a mass spectrometer.
Procedure
Run the "Charged Particles" MS DOS program, from Vernier Software. On the Main Menu, you'll find eight challenges.
Do Challenges #1, 2, 3, and 8 (in order), completing the attached worksheets. The program is keyboard oriented--the
mouse will not work. The menu at the bottom of each screen suggests what keys to use. To increase the magnetic field
you'll push the B key; to decrease it. use [Ctrl] B. Table #1 will be helpful in figuring out the unknown in the Mass
Spectrometer exercise of Challenge 8. The following data will be useful in the other challenges:
mass of electron= 9.11 x 10-31 kg; charge on electron = 1.602 x 10-19 C;
mass of alpha particle = 6.6465 x 10-27 kg
-27
-19
mass of proton = 1.67 x 10 kg;
charge on proton = 1.602 x 10 C;
charge of alpha particle = 3.204 x 10-19 C