The objective of this experiment is to measure the charge to mass ratio, (e/m), of the...
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The objective of this experiment is to measure the charge to mass ratio, (e/m), of the elec- tron. This will be done by using a special (e/m) apparatus which consists of an electron tube and a set of Helmholtz coils. The student will directly measure the accelerating volt- age, V, the coil current, I and the radius of the electron beam path, r. The calculated value of (e/m) will be compared with the accepted value. II. APPARATUS (e/m) apparatus, 2 power supplies, 2 multimeters and connecting wires. III. THEORY 1. The electron was discovered by the British physicist Sir J. J. Thomson (1856-1940) in the year 1897. Its charge and mass have the accepted values (four significant figures) e 1.602 x 10-19 C and m = 9.109 x 10-31 kg. Thus the accepted value of the charge to mass ratio is (e/m) 1.759 x 101 C/kg (1) 2. In the apparatus of this experiment, as the electron travels from the cathode to the anode, it is accelerated through a potential difference V. Thus its potential energy decreases by an amout eV and its kinetic energy increases by the same amount. This can be written as eV = mu. (2) 3. The magnetic field of the Helmholtz coils exerts a force on the electron Feux B. This force bends the electron beam into a circle of radius T= eB (3) Solving equations (2) and (3) for (e/m) (notice v is velocity and V is voltage) gives e 2V m B22 (4) 4. In this experiment, you will directly measure the accelerating voltage, V, the radius of the electron path, r, and the coil current, I. From the current, the magnetic field will be calculated using equation (5), then e/m will be calculated from equation (4). IV. EXPERIMENTAL PROCEDURE 1. CAUTION: THE APPARATUS SHOULD BE OFF WHEN NOT TAKING DATA. 2. The lab assistant or the instructor will wire the apparatus. In the circuit there should be a voltmeter to measure the accelerating voltage V and an ammeter to measure the coil current, I. 3. Turn the power supplies on. Turn the voltage up until the voltmeter reads about 250 V. Observe the electron beam. 4. Turn the current up and watch the electron beam bend in a semicircular arc. Adjust the current until the outer edge of the beam hits the 10 cm mark on the horizontal scale. When this happens, the scale will glow green. Record the value of the current in your data table. 5. Note (1): The electron beam should not get too close to the glass tube. Note (2): This is a visual observation and its accuracy is crucial to the success of this experiment and therefore must be made very carefully. 6. Notice that the horizontal scale is not really horizontal. It is tilted down. This means that the radius of the electron beam is larger than the radius you measured by a small amount. To take this into account, we will assume the actual radius is 10% larger than the one measured. Therefore the value of the beam radius will be adjusted upward by 10% to a value of r = 0.055 m. 7. Since the measurement of r, the radius of the electron beam is the difficult part of this experiment, and doing this measurement accurately is crucial to the success of this experiment, it is good practice to choose values of V and a corresponding I such that the beam radius remains constant. This is what we will do. 8. When you are finished taking all the data, turn the power supplies and the multimeters off and leave the circuit connected. Proceed to the analysis section. 9. The number of turns in each coil is given N = 130 and the coil radius is Rcoil 0.150 m. = 2 Experiment (8) Data Table N = 130, Rcoil = 0.150 m Accelerating Coil Current Beam Diameter Beam Radius Magnetic Field Voltage I81 ddd r B V8V (A) (m) (Volts) (m) (m) (T) -4 22110.5 1.23 0.005 0.10.05 0.050.005 9.5910 2410.5 1.330.005 -3 0.10.05 0.05+ 0.005 1.04x10 281 0.5 1.40 0.005 0.10.05 0.050.005 1.09103 -3 2000.5 1.450.005 -3 0.10.05 0.050.005 1.1310 2310.5 1.52 0.005 0.10.05 0.050.005 1.18 10 3 e Experiment (8) Data Table 2V = (1/4) B (Br)2 (Volts) (Tm) 2442 2.30109 502 2.70410 9 5622 -9 2.9710 -9 600 3.1910 662 Slope of line % difference = 1.8810" 85 7% 3.48109 8. Calculate the relative uncertainty in B from the recorded uncertainty of I and Rcoil for one of the data points. 9. Extra Credit: Derive the expression for the magnetic field of a Helmholtz coil. This is equation (5). Hint: The magnetic field of a current loop at point P on the axis of the loop at a distance y from the plane of the loop is given by equation (12.15) in your textbook. B = wire I sin Odx r2 12.5 The objective of this experiment is to measure the charge to mass ratio, (e/m), of the elec- tron. This will be done by using a special (e/m) apparatus which consists of an electron tube and a set of Helmholtz coils. The student will directly measure the accelerating volt- age, V, the coil current, I and the radius of the electron beam path, r. The calculated value of (e/m) will be compared with the accepted value. II. APPARATUS (e/m) apparatus, 2 power supplies, 2 multimeters and connecting wires. III. THEORY 1. The electron was discovered by the British physicist Sir J. J. Thomson (1856-1940) in the year 1897. Its charge and mass have the accepted values (four significant figures) e 1.602 x 10-19 C and m = 9.109 x 10-31 kg. Thus the accepted value of the charge to mass ratio is (e/m) 1.759 x 101 C/kg (1) 2. In the apparatus of this experiment, as the electron travels from the cathode to the anode, it is accelerated through a potential difference V. Thus its potential energy decreases by an amout eV and its kinetic energy increases by the same amount. This can be written as eV = mu. (2) 3. The magnetic field of the Helmholtz coils exerts a force on the electron Feux B. This force bends the electron beam into a circle of radius T= eB (3) Solving equations (2) and (3) for (e/m) (notice v is velocity and V is voltage) gives e 2V m B22 (4) 4. In this experiment, you will directly measure the accelerating voltage, V, the radius of the electron path, r, and the coil current, I. From the current, the magnetic field will be calculated using equation (5), then e/m will be calculated from equation (4). IV. EXPERIMENTAL PROCEDURE 1. CAUTION: THE APPARATUS SHOULD BE OFF WHEN NOT TAKING DATA. 2. The lab assistant or the instructor will wire the apparatus. In the circuit there should be a voltmeter to measure the accelerating voltage V and an ammeter to measure the coil current, I. 3. Turn the power supplies on. Turn the voltage up until the voltmeter reads about 250 V. Observe the electron beam. 4. Turn the current up and watch the electron beam bend in a semicircular arc. Adjust the current until the outer edge of the beam hits the 10 cm mark on the horizontal scale. When this happens, the scale will glow green. Record the value of the current in your data table. 5. Note (1): The electron beam should not get too close to the glass tube. Note (2): This is a visual observation and its accuracy is crucial to the success of this experiment and therefore must be made very carefully. 6. Notice that the horizontal scale is not really horizontal. It is tilted down. This means that the radius of the electron beam is larger than the radius you measured by a small amount. To take this into account, we will assume the actual radius is 10% larger than the one measured. Therefore the value of the beam radius will be adjusted upward by 10% to a value of r = 0.055 m. 7. Since the measurement of r, the radius of the electron beam is the difficult part of this experiment, and doing this measurement accurately is crucial to the success of this experiment, it is good practice to choose values of V and a corresponding I such that the beam radius remains constant. This is what we will do. 8. When you are finished taking all the data, turn the power supplies and the multimeters off and leave the circuit connected. Proceed to the analysis section. 9. The number of turns in each coil is given N = 130 and the coil radius is Rcoil 0.150 m. = 2 Experiment (8) Data Table N = 130, Rcoil = 0.150 m Accelerating Coil Current Beam Diameter Beam Radius Magnetic Field Voltage I81 ddd r B V8V (A) (m) (Volts) (m) (m) (T) -4 22110.5 1.23 0.005 0.10.05 0.050.005 9.5910 2410.5 1.330.005 -3 0.10.05 0.05+ 0.005 1.04x10 281 0.5 1.40 0.005 0.10.05 0.050.005 1.09103 -3 2000.5 1.450.005 -3 0.10.05 0.050.005 1.1310 2310.5 1.52 0.005 0.10.05 0.050.005 1.18 10 3 e Experiment (8) Data Table 2V = (1/4) B (Br)2 (Volts) (Tm) 2442 2.30109 502 2.70410 9 5622 -9 2.9710 -9 600 3.1910 662 Slope of line % difference = 1.8810" 85 7% 3.48109 8. Calculate the relative uncertainty in B from the recorded uncertainty of I and Rcoil for one of the data points. 9. Extra Credit: Derive the expression for the magnetic field of a Helmholtz coil. This is equation (5). Hint: The magnetic field of a current loop at point P on the axis of the loop at a distance y from the plane of the loop is given by equation (12.15) in your textbook. B = wire I sin Odx r2 12.5
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Digital Systems Design Using Verilog
ISBN: 978-1285051079
1st edition
Authors: Charles Roth, Lizy K. John, Byeong Kil Lee
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