Determination of the Electron s Charge-to-Mass Ratio, e/m

Transcription

1 Determination of the Electron s Charge-to-Mass Ratio, e/m Figure 1. Bent Electron Beam Purpose: To study the behavior of electrons in electromagnetic fields, and to determine the ratio e/m (the "specific electronic charge"). Equipment: Teltron 55 Deflection e/m Tube Teltron 50 Helmholtz Coils Teltron 501 Universal Stand Teltron 813 High Voltage Power Source DIGI 35A Power Supply Digital Multimeter Patch Cords Theory: In this experiment we will use a cathode ray gun as a source of electrons. The electrons are accelerated to a velocity, v, by the potential difference V a (anode voltage). The speeding electrons then enter the bulb of the Teltron tube where electric and magnetic fields can be applied to the electron beam. If V a is fixed the electron velocity is also fixed. When a current, I, passes through the Helmholtz coils, a fairly uniform magnetic field is generated in the bulb: B = αi where 1 of 9

2 3 α = The coils are arranged so that B is perpendicular to v and so the path of the electrons is circular, with radius of curvature r: and hence mv = q v B = ma = Eq. 1 r F B Therefore, if we know I and r we could determine e/m if we know the velocity, v. e m = v rb Eq. There are two methods to determine the velocity. One method is to consider the relationship between the accelerating voltage, V, and the kinetic energy: K = 1 mv. q V = 1 mv Eq. 3 Setting q = e and substituting into Eq., gives: e m V = Eq. 4 r α I To determine v in Eq. another way, we will apply an electric field, E, and a magnetic field B such that F E = -F B. Thus, a = 0 and v = constant. Note that we want the same Va as before in order to measure the same v. This method can be thought of as the "crossed electric and magnetic fields method." To understand this method, consider the that the electrons will move in a straight line if F = F and hence E B e E = evb E v = Eq. 5 B By combining Eqs. and 5 and measuring r, B, E and B, the ratio e/m can be determined. Experiment: CAUTIONS & WARNINGS before you begin: It is VERY IMPORTANT that you read the following: The potential difference V a that accelerates the electrons is on the order of 3000 V. This is dangerous and caution must be observed. of 9

3 Therefore, in all procedures in this lab, YOU MUST: A. Keep calm and think before you reach for something. B. Always dial down the voltage using the lever and turn to OFF the switch on the back of the kilovolt power supply while making any changes in the circuit or if you are not at that moment making an observation! Part A: Measuring the Electron Beam Radius In this section of the laboratory, you will accelerate the electrons using an AC source to boil electrons off the Teletron tube cathode. Then a high voltage power supply will be applied to accelerate the electrons past a pair of horizontal deflecting plates. An electric field will be applied across these plates (also controlled with the high voltage power supply). A magnetic field will be established in the Helmoltz coils (using an entirely different circuit and low voltage power supply). Finally, the electric and magnetic fields will be varied and measured, along with the resulting deflection and radius of the electron beam. Figure 3. Basic Circuit Diagram for Experimental Apparatus 1. Assemble the Deflection e/m Tube, Helmholtz Coils, Universal Stand, Power Supplies, DMM, and Decade Box as shown in Figure and Figure 3. It is important to line up the Helmholtz magnetic coils perpendicular to the Earth s magnetic field in order to reinforce the magnetism s effort to straighten out the electron beam.. Figure 3 is a schematic diagram of this set-up. Connect the DIGI Power Supply to the Helmholtz Coils. This set up provides DC current through the Helmholtz Coils to establish the magnetic field. 3. The electrical lead from the Decade Box should connect to the DMM s Amps jack, and the DMM s Common/Ground jack should connect to the A terminal of the first coil. Set the DMM function to Amps. 3 of 9

4 4. Connect the 6.3 VAC terminals on the High Voltage Power Supply to the 4 mm sockets in the plastics cap at the end of the tube s gun. This connection provides power to the anode filament. The filament current boils off electrons providing a source of electrons for the gun. 5. Connect the positive + terminal of the High Voltage Power Supply to the plugs mounted on the side of the gun s neck. This connection to the anode of the gun provides the accelerating potential V a. 6. Also connect the positive + terminal of the High Voltage Power Supply to the 4 mm plugs connected to the deflection plates. Note that the plates are at the same potential and hence there is no E Field. 7. Connect the Power Supply s negative - terminal to the gun socket marked - to provide a common return path 8. Turn on the Digi 35A Power Supply and gradually adjust the voltage for a DMM reading of about 300 ma. Record the coil current I. You should not exceed A of current under any circumstances. 9. Turn on the High Voltage Power Supply and slowly increase V a to 500 V by reading the top scale of the supply s meter. 10. Note the deflection of the electron on the luminescent screen. In order to determine r, the radius of curvature of the electron path, record X and Y for three points fairly far out on the curve. 11. Decrease the voltage to zero and turn off the High Voltage Power Supply. Part B: Crossed Electric and Magnetic Fields In this section of the lab you will first determine the electron velocity by providing crossed electric and magnetic fields of the proper magnitude to allow the electron to move through without deflection. In this case, the electric field is provided across the horizontal deflection plates within the Teletron tube. The magnetic field is produced by the Helmoltz coils. Finally, the high voltage power supply applies the accelerating voltage, which in turn determines the electron velocity. A schematic diagram of the connections for both the Helmholtz coils and the Teletron tube is shown in figure 4 below: 4 of 9

5 Figure 4: Crossed Electric and Magnetic Fields (F B = F E Configuration) 1. To measure the velocity, v, of the electron, set up the circuit as shown in Figure 4. This circuit differs from the previous set up in that the bottom deflection plate in connected to the positive + terminal of the High Voltage Power supply and the top deflection plate is connected to the negative - terminal of the HV Power Supply. Note that an electrostatic field is set up across the deflection plates.. Turn on the High Voltage Power Supply and gradually increase V a to 500. (Hence, the velocity, v, is the same as before.) 3. Change the coil current, I, (and hence B) by changing the decade resistance until the path of the electrons is as straight as possible. Record the new current, I. Do not exceed A under any circumstances. 4. Decrease V a to zero and turn off the High Voltage power supply and the Low Voltage Power Supply. 5 of 9

6 Analysis: 1. To determine r, the radius of curvature, consider the equation of a circle located as shown: r y x 0,0 The equation of such a circle is x + y x + ( y r) = r r = y However, this assumes that the x-coordinates are measured from the origin. 6 of 9

7 Before substituting your x and y values into this equation, add +0.5 cm to the x- values. Calculate r for each pair. Calculate r average.. Use the results of Part A, and Eq. 4 to determine e/m. 3. Now you will make use of the "crossed electric and magnetic fields" method. First, substitute Eq. 5 into Eq. to derive an expression for e/m in terms of the values from Part B. Substitute for B, B and E in terms of I, I, V a and d using B = αi and V a E = where d is the separation of the plates. d 4. Calculate e/m using the observed values I, I, V a, d, and r, and compare to the accepted value. 5. The main goal in this experiment is to measure a well known physical quantity and compare your results with those of previous experiments (resulting in the values posted in physics texts). Write at least one paragraph discussing the following: How did your results compare to the accepted value? Is the accepted value within your uncertainty range? What errors and problems, both systematic and random prevented a better value? If you could improve the design and equipment to improve the accuracy and precision for this measurement, how would you do so? Results: Write at least one paragraph describing the following: what you expected to learn about the lab (i.e. what was the reason for conducting the experiment?) your results, and what you learned from them Think of at least one other experiment might you perform to verify these results Think of at least one new question or problem that could be answered with the physics you have learned in this laboratory, or be extrapolated from the ideas in this laboratory. 7 of 9

8 DATA and ANALYSIS TABLES Part A: Coil Current, I: x y r r avg e/m: δ (e/m): Part B: Coil Current, I: Plate Separation, d: derivation: e/m: explain: 8 of 9

9 accepted value of e/m: % difference: agreement within uncertainty? 9 of 9