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In this section of the lab, you will use the large apparatus to produce a beam of electrons and measure the effect of an applied magnetic field on the trajectory of the beam. As you have seen, a magnetic field can be created by the large rings of current (Helmholtz coils) above and below the glass globe. In each of these coils the current is in the same direction. The two rings of current are similar to the two permanent magnets you experimented with in Section A. Which magnet orientation (aligned magnetic dipole moments or anti-aligned magnetic dipole moments) is similar to the Helmholtz coils? Connecting the experiment The first step in creating the electron beam is to eject them from a metal filament. To do this, the filament is heated by passing a current of about 10 mA though it. Connect the Filament outputs to the top and bottom connections on the Teflon plastic connector block on the end of the glass globe. • The second step in creating the beam is to give the electrons some speed by accelerating them through a potential difference. This is done by applying an 'accelerating' voltage between the filament and the cylindrical anode. Do this by connecting a banana plug cable between the Anode output and the side' connection on the Teflon plastic connector block. • The accelerated electron beam escapes through a rectangular slit in the anode. They are moving at a speed v determined by the accelerating potential AV. Filament Anode Accelerated electron beam t DV Filament Anode Filament top connection bottom connection C2. What is the velocity of an electron accelerated from rest through a 22V potential? side connection C3. If the accelerating potential doubles, by what factor does the electron's velocity change?
Now turn on the power supply. At this point you should have in place the connections to produce the electron beam, but not yet connected to the Helmholtz coils. Set the ANODE Volts switch to 22 V. Supply filament current by turning up the knob below the "ANODE milliamps" display all the way to its maximum value. The "Filament On" lamp should light. You should see the ionization path from the electron beam (dimming the lights helps). C4. Use one of the cylindrical magnets to steer the electron beam (hold it up to the glass globe and move it around). What is happening? Imagine the pattern of field lines from the magnet to determine the sign of the magnetic field at the electron beam. Turn the cylindrical magnet upside down to check your reasoning. C5. Now connect the "Field" outputs to the banana-plug connections on the Helmholtz coils, and increase the current to the coils until "FIELD Amps" reads about 2 Amps. What are the electrons doing? Vary the field and observe the results. Reverse the field direction by changing the current leads (turn the current down to zero before reversing the leads) and observe the results. Explain. C6. Set the current in the coils to the direction that gives a circular orbit for the electrons. Set the accelerating potential to 44V by flipping the switch under the "ANODE Volts" display. What happens to the orbit? Explain. C7. Return the anode voltage to 22V and adjust the magnetic field so that the beam of electrons hits each of the "cross-bars". Crossbar No. 1 2 3 Distance to Filament 0.065 m 0.078 m 0.090 m 0.103 m 0.115 m Radius of Beam Path 0.0325 m 0.039 m 0.045 m 0.0515 m 0.0575 m Do you need to increase or decrease the field to go from crossbar 5 to crossbar 1? Why? C8. Adjust the magnetic field so that the beam hits crossbar 2. What is the current through the coils? Record it on your whiteboard. C9. Unfortunately, you can't directly measure the magnetic field at the center of the globe with your Pasco sensor. However, this particular apparatus is configured such that the field at the center of the globe is related to the current through the by Bcenter = (1.96 x 10-4) loop Using this relation, determine the magnetic field at the center of the globe for the current you recorded in C8.
D. Challenge: Measuring the ratio e/m for the electron Your task is to use the electron beam apparatus to measure a characteristic value, the charge-to- mass ratio of the electron, e/m. Here are some ideas to get you started: • The centripetal force is given by Fe acting on the electrons in this situation? mv² What force is providing the centripetal force • The Earth produces its own magnetic field, and the local magnitude of that field is about 5.5 x 10-5 T. Would you expect this to affect your results in a measurable way? Try to quantify how much of an effect it might have.