In this experiment students will use the PASCO Model SE-9638 e/m apparatus to investigate the motion of electrons in the presence of electric and magnetic fields. Students will determine the electron's charge to mass ratio e/m by measuring the radius of curvature of an electron's path in a uniform magnetic field of known strength.
In the PASCO Model SE-9638 e/m apparatus a beam of electrons is accelerated through a known potential difference, so the kinetic energy and therefore the velocity of the electrons is known. A pair of Helmholtz coils can produce a uniform magnetic field at right angles to the electron beam. This magnetic field then deflects the electron beam in a circular path. A unique feature of the e/m tube is that the socket rotates, allowing the electron beam to be oriented at any angle (from 0-90 degrees) with respect to the magnetic field produced by the Helmholtz coils. The vector nature of the magnetic force on moving charged particles can therefore be explored. A small permanent magnet can also be used to deflect the electron beam. The e/m apparatus also has deflection plates that can be used to demonstrate the effect of an electric field on the electron beam.
 | The e/m Tube The e/m tube is filled with helium at a pressure of 10-2 mm Hg. It contains an electron gun and deflection plates.
The electron beam leaves a visible trail in the tube, because some of the electrons collide with helium atoms. The atoms are excited and then radiate visible light. The electron gun is shown in the figure below.
The heater heats the cathode, which emits electrons. The electrons are accelerated by a potential difference between the cathode and the anode. The grid is held positive with respect to the cathode and negative with respect to the anode. It helps to focus the electron beam. |
| The Helmholtz Coils The radius of the coils is equal to their separation. This geometry provides a highly uniform magnetic field near the center of the coils. The Helmholtz coils of the e/m apparatus have a radius and a separation of 15cm. Each coil has 130 turns. The magnetic field B produced by the coils is proportional to the current I through the coils times 6.6´10-4T/A. It is perpendicular to the plane of the coils. |
B = (6.6´10-4T/A)I.
| The Controls The control panel of the e/m apparatus is straightforward. All connections are labeled. |
| Cloth Hood The hood can be placed over the top of the e/m apparatus so the experiment can be performed in a lighted room. |
| Mirrored Scale A mirrored scale is attached to the back of the rear Helmholtz coil. It is illuminated when the heater of the electron gun is powered. By lining the electron beam up with its image in the mirrored scale, the radius of the beam path can be measured without parallax error. |
Part I: Measuring e/m
| Power supplies and meters are connected to the to the front panel of the e/m apparatus, as shown
in the figure below.
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| The power supplies are adjusted to the following levels:
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| The current for the Helmholtz coils is adjusted with the current adjust knob. The ammeter displays the current in units of Ampere (A). |
| After the cathode has heated up, the electron
beam emerges from the electron gun. Its path is curved by the field from the
Helmholtz coils. The electron beam's path is parallel to the Helmholtz coils.
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| Carefully read the current to the Helmholtz coils from the ammeter and the acceleration
voltage from the voltmeter in the picture below. Record the values in the table
1.
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Table 1
| Current to coils I (A) |
Accelerating voltage (V) |
Magnetic field B= (6.6´10-4T/A)I |
Radius of circular path r (m) |
e/m= 2V/(Br)2 |
| Carefully measure the radius of the circular path of the electron beam.
Look through the
tube at the electron beam. Measure the
radius of the path as you see it on both sides of the scale, then average the results.
(The markings on the scale are in units of cm.) Record your result in the table.
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The magnetic force Fm acting on a charged particle of charge q moving with velocity v in a magnetic field B is given by the equation Fm = qv´B. Since the electron beam in this experiment is perpendicular to the magnetic field, we have the following equation relating the magnitudes Fm, q, v, and B.
Fm = qvB.
The electron is moving in a circular path of radius r, with the magnetic force being equal to the centripetal force mv2/r. We therefore have
qvB = mv2/r or q/m = v/Br.
We denote the magnitude of the charge q of the electron by e and therefore have
e/m = v/Br.
The electrons are accelerated through the accelerating potential V, gaining kinetic energy equal to their charge times the accelerating potential. Therefore eV=(1/2)mv2. The velocity of the electrons therefore is v=(2eV/m)1/2. Inserting this expression for v in the equation above we obtain
e/m = 2V/(Br)2.
| Calculate e/m (in units of C/kg) from the measured values in your table. | ||
| Calculate e/m from the accepted values of the electron's charge and mass.
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Part II: Electrons moving in a magnetic field
| The socket for the e/m tube is designed so that the tube can be rotated through 90
degrees. The tube can therefore be oriented so it is at any angle, from 0-90 degrees, with
respect to the magnetic field from the Helmholtz coils. In the movie
clip below the tube is being rotated. Move the cursor over the video clip to
start the movie.
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| In the movie clip below the current to the Helmholz coils is being
adjusted. Move the cursor over the video clip to start the movie.
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| Instead of using the Helmholtz coils to bend the electron beam, you can use a permanent
magnet to show the effect of a magnetic field on the electron beam. In
the clip below, a south pole is brought close to the beam. Move the cursor over the video clip to
start the movie.
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| In the clip below, a north pole is brought close to the beam. Move the cursor over the video clip to
start the movie.
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Open Microsoft Word and prepare a report using the template shown below.
| Summarize the experiment. |
| Insert your table and answer all the questions posed in the procedure and data analysis sections. |
Save your Word document (your name_lab9.doc) and attach it to an e-mail message to mbreinig@utk.edu.
