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Illinois State University Department of Physics Physics 112 Physics for Scientists and Engineers III Experimental Physics Laboratory 3 The charge to mass ratio of the electron Introduction At the end of the 19th century, a number of observations, including the ultra-violet catastrophe, photoelectric effect, and existence of atomic spectra, suggested that the classical theories of the day were incomplete or deficient. In 1897 J. J. Thompson showed that the charge to mass ratio of an electron was a constant, establishing the electron as a fundamental particle. More details can be found in Chapter 29 of Serway and Jewitt (6 th ed.) [1] or almost any modern physics textbook. Schuster's method is used in this experiment and more information can be found in the Taylor manual [2]. The basic idea is to take electrons of known kinetic energy and determine the required B field to force them into a circular trajectory of a specified radius. The charge to mass ratio can be calculated from the results. Helmholtz coil looking down the axis 5 pins Filament accelerating grid Electron tube Figure 1. A schematic of the set-up is shown in Fig. 1. It consists of an electron tube containing a filament to emit electrons, an accelerating grid used to control the kinetic energy of the electron beam, and a set of 5 pins used to determine the radius of the electron beam trajectory. The outer circle represents the Helmholtz coil that is used to generate a magnetic field pointing out of the page in the diagram. Electrons with mass m emitted by the filament are accelerated through a potential difference V maintained between the filament and accelerating grid, yielding a kinetic energy, 1 2 KE=eV = m v , 2 (1) where v is the velocity of the electron. The electrons are then acted upon by a magnetic field produced by a Helmholtz coil, which is actually two coils. The magnetic field B exerts a force of magnitude F B =−e v B , where the velocity and B field vectors are perpendicular to each other. This force causes the electrons to travel in a circular trajectory of radius r, so the force is centripetal, evB= mv 2 . r Combining these results, the charge to mass ratio is e 2V = . m r 2 B2 Of course this requires calculating the value of the B field component directed along the axis of the Helmholtz coil. We can consider the Helmholtz coil to consist of two rings of current with radius R =147.5 mm and separated by a distance R, each with a current that is N =124 times the current in the wire since there are 124 loops in each half of the coil. Consequently, the electrons are R/2 from each loop of the Helmholtz coil. The resulting B field along the axis is 3 4 ( 2 ) μ0 N I . B=( ) ( ) 5 R Adjustment of the accelerating voltage and coil current allows the trajectory of the electron beam to be varied. The radii of the trajectories are 10, 20, 30, 40, and 50 mm when the electron beam intersects the planes of the pins. A wiring diagram of the experimental set-up is shown in Fig. 2. Be careful if you have to wire up your own circuit and ask the instructor to check your wiring before plugging in the power supply. Also confirm that all knobs on the power supply are turned all of the way in the counter-clockwise direction. The filament voltage should be set to 9 V. The coil voltage will be adjusted throughout the experiment as needed to make the electron beam follow a circular path. The kinetic energy of the electrons is determined by the KE voltage and should be set to 100 volts at the beginning of the experiment. Finally, the focus voltage is adjusted as needed to create the best defined electron beam. The electron beam appears orange because electrons transfer energy to neon gas in the electron tube and the excited neon atoms emit the orange light. ammeter Electron Tube Base Power Supply A KE Focus Coil Filament Figure 2. Objective In this exercise, you will determine the charge to mass ratio of the electron and analyse the various contributions to the uncertainty in your measurements and results. Procedure Begin by connecting the circuit as shown in Fig. 2. After your instructor has approved your circuit wiring, you may begin the experiment. For accelerating voltages of 100 V, 150 V, 200 V, 250 V, and 300 V, determine the coil voltage and current required to make the electron beam intersect the plane of each set of pins in the electron tube. The coil current cannot be raised to the level required to force the electrons to reach some of the pins. Derive an equation that allows you to do a linear fit of accelerating voltage as a function of the product of pin position and coil current. Fit your data with this equation and determine the charge to mass ratio. Do not calculate the charge to mass ratio for each individual measurement. Generally, it is a good idea to record every measurable quantity for each set of parameters. There are several ideas that you might want to explore when writing your lab report. For example, what is the effect of the earth's magnetic field? How does the force that it exerts on the electron beam compare to the coil generated field? What sort of error is present when determining the uncertainty of the beam position? Is the error caused by the resolution of a meter display or by the sighting mechanism in the electron tube? Perhaps it is caused by some other factor. Is there a systematic error? Remember, just stating a cause of uncertainty is of little value. You must show my numerical analysis its magnitude and what it means for your data and results. References [1] Serway, R. A., and Jewett, J. A. Jr. Physics for Scientists and Engineers with Modern Physics, Thomson, 6th ed. (2004). [2] Brown, T. B. ed. The Lloyd William Taylor Manual, Addison-Wesley, 1959.