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name____________________ period _______ lab partners___________________________________ 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