- P Ybaseline Yobs Two Values For Two Polarity Method 25cm 75 Cm I Com Acm B5cm 1 25cm 1 5cm 5cm 1cm 7 2cm 3 33 1 (46.98 KiB) Viewed 31 times
- P Ybaseline Yobs Two Values For Two Polarity Method 25cm 75 Cm I Com Acm B5cm 1 25cm 1 5cm 5cm 1cm 7 2cm 3 33 2 (52.11 KiB) Viewed 31 times
- P Ybaseline Yobs Two Values For Two Polarity Method 25cm 75 Cm I Com Acm B5cm 1 25cm 1 5cm 5cm 1cm 7 2cm 3 33 3 (81.09 KiB) Viewed 31 times
- P Ybaseline Yobs Two Values For Two Polarity Method 25cm 75 Cm I Com Acm B5cm 1 25cm 1 5cm 5cm 1cm 7 2cm 3 33 4 (64.96 KiB) Viewed 31 times
- P Ybaseline Yobs Two Values For Two Polarity Method 25cm 75 Cm I Com Acm B5cm 1 25cm 1 5cm 5cm 1cm 7 2cm 3 33 5 (64.96 KiB) Viewed 31 times
- P Ybaseline Yobs Two Values For Two Polarity Method 25cm 75 Cm I Com Acm B5cm 1 25cm 1 5cm 5cm 1cm 7 2cm 3 33 6 (70.2 KiB) Viewed 31 times
FIELDS 88 EXP. 11. ELECTRON ACCELERATION AND DEFLECTION BY ELECTROSTATIC 4. Repeat this procedure using power supply voltages of 2.5,3.0, and 3.5 kV. On your data shee sketch the electron beam path you see. 11.5 Analysis 11.5.1 FD analysis First you must correct your set of y values using your chosen method. . If you chose "baseline subtraction", find the baseline correction for y for each data point. Note that this will depend on x. Your corrected y Yobserved baseline is the vertical position (deflection) you will plot and use to find Fp. If you used the "two polarity" method, calculate the deflection as half the difference of the two y values recorded at each x. If y vertical deflection of the beam, y, is the position with top plate positive, and y. is the position with the top plate negative, then y=(---). The equation should be used only by those using the two polarity method. Either method will result in a set of corrected (x,y) values representing the path of the deflected beam. From this point the analysis is the same for both methods. Hints for data analysis 1. Plotting y vs. x for 0 deflection = Baseline correction ya 2. Plot y vs. 1 3. Ploty-ya vs. x (Corrected y) 4. Calculate Error on y-ya 5. Calculate Fp and Error (See below) Example: plot y vs ² for Fp calculation Make a graph of y vs. x². Indicate the uncertainties in the points with error bars. The uncertainty in the vertical position (ay) involves propagation of errors for a sum, and the uncertainty in is given by 02=2x0₂ This plot should yield a straight line. Draw the best straight line for the graph. Calculate the slope and set it equal to Fp/4s. Calculate Fp and its uncertainty, oy. You will need Fo for the Thompson Experiment below. 11.5.2 Thompson analysis 1. For Thompson's experiment, calculate e/m ratio for each trial. 2. Calculate an average and standard deviation of these e/m values. This will be your result using the Thompson method. Because the beam did not follow a straight path, we consider that this part is only a qualitative measure of e/m. 3. The accepted value of e/m is 1.76 x 10¹1 C/kg. Compare your results from both methods to this value.
11.4.1 Baseline and Fp measurement Once you are cleared for beam on (high voltage) measurements, set Vps to 2000 V, and begin record- ing beam positions (x, y points). Take y as the vertical position of the center of the beam at each chosen x. Be sure to take into account the sign of the y value. The uncertainties o, and oy must be es- timated from your ability to interpolate between graticule lines in light of the finite beam width. You will need to decide which method ("baseline subtraction" or "two polarity") to use for alignment error correction. . 1. If using "baseline subtraction" start with an undeflected beam. Do this by connecting both deflector plates to the same voltage as the anode. With beam on, verify that the beam is a straight line and measure a pair of points, one near the anode, and the other near x = 10 cm. 2. Fp measurement. With the baseline data measured, turn the high voltage off, and recon- figure the deflection plate voltages to provide Vplate= Vps between them. Turn the high voltage back on, and record at least 10 (x,y) pairs along the path of the deflected beam. Use as large a span of x as you can. 1. If using the "two polarity" method, configure the deflection plate voltages to provide Vplate= Vps. Do this by connecting one plate to the anode voltage, and the other to the cathode voltage. Turn the high voltage back on, and record at least 10(x, y) pairs along the path of the deflected beam. Use as large a span of x as you can. Turn the high voltage off, reverse the polarity of your deflection plates, and turn the high voltage back on. The sense of deflection should be reversed. 2. Fp measurement. For every x value, calculate the average position y for your two polarity readings. This will be the baseline measurement baseline Now subtract that from either one of the polarity readings to get the values for y. For better error reduction use the largest span of x and y values possible. 11.4.2 Thompson's Experiment Record your values of the distance between the plates, s, and the geometric correction factor, FD. Make sure all power supplies are turned off. Reconfigure the experiment with deflection plates having voltage Vps Vplate For the polarity of the electric field, we want it set so that it deflects the beam in the direction opposite to the direction of bend by the magnetic field. Have the instructor inspect your reconfigured setup before turning any power back on. Now you are going to measure e/m by balancing the electric field with the magnetic field. 1. Connect Pg to Fx2 (Fig. 11.4). Set Vps to 2000 V. 2. Supply current to the Helmholtz coil and adjust the current to get a straight line. (The B field should act opposite to the E field. Reverse the coil current if necessary.) Adjust the current in the coils until the beam is as straight as possible though it will not be a perfect straight line. This can be attributed to the small plates and small coils: The electric and magnetic fields are not really constant, but vary near the edges of the apparatus. To get your best results in this part, you should seek a level beam near the center of the graticule, even if it is a few millimeters below (or above) the centerline. Since the beam does curve, first one way, then the other, try to make the tangent to the path level as your criterion. 3. Once a level tangent is achieved, record your values for Vps and I.
11.7. DATA SHEET 91 11.7 Data sheet Name: Date: Instructor's initials: Deshaun T. Partner: Group No: Data Vi y2 = b cm 13 cm Xobs Уbaseline y = Yobs-ybaseline 25cm 1. Baseline measurement (section 11.4.1) Point near anode x1 = cm Point near 10 cm 1 Ocm Fit to y = ax + b 2. Electron deflection (section 11.4.1) Yobs (two values for two polarity method) z . 75 cm Locm 73 1.5cm -scm 2cm ICM 5 3.33.4m I. SCM 5cm -Z..CA Z 6.5 -300 9 cm - 3-SCO 오 11.500 -5s.ca 10 14.30m, 1cm 1,25 cm, مگر سی (a) Measure the distance between the plates s = (b) Graph y vs. x2, include error bars. Measure the slope of the graph, slope = (c) From the slope, calculate the correction factor FD = 3. Thompson's Experiment (section 11.4.2) Record voltage and current for 4 settings: Vps (kV) 2.00 3.00 6 3-90 I (A) .24 A .40 A SC 72 B (T) e/m (C/kg) Sketch the path of the beam: 2.5Q y
T 11.4.1 Baseline and Fp measurement error correction . cm. Once you are cleared for beam on thigh voltage) measurements, set Vis to 2000 V, and begin record ing beam positions points). Take y as the vertical position of the center of the beam at each chosen x. Be sure to take into account the sign of the y value. The uncertaintiese, and o, muitbeer timated from your ability to interpolate between graticule lines in light of the finite beam width You will need to decide which method ("baseline subtraction" or "two polarity) to use for alignment 1. If using "baseline subtraction start with an undeflected beat. Do this by connecting both deflector plates to the same voltage as the anode. With beam on, verify that the beam is a straight line and measure a pair of points, one near the anode, and the other near x = 10 2. Fp measurement. With the baseline data measured, turn the high voltage off, and recon figure the deflection plate voltages to provide Vplate - Vps between them. Turn the high voltage back on, and record at least 10 (x,y) pairs along the path of the deflected beam. Use as large a span of x as you can 1. If using the "two polarity" method, configure the deflection plate voltages to provide Vplate - Vps. Do this by connecting one plate to the anode voltage, and the other to the cathode voltage. Turn the high voltage back on, and record at least 10(x,y) pairs along the path of the deflected beam. Use as large a span of x as you can. Turn the high voltage off, reverse the polarity of your deflection plates, and turn the high voltage back on. The sense of deflection should be reversed. 2. Fp measurement. For every x value, calculate the average position y for your two polarity readings. This will be the baseline measurement baseline. Now subtract that from either one of the polarity readings to get the values for y. For better error reduction use the largest span of x and y values possible 11.4.2 Thompson's Experiment Record your values of the distance between the plates, s, and the geometric correction factor, Fp- Make sure all power supplies are turned off. Reconfigure the experiment with deflection plates having voltage Vps = Uplate For the polarity of the electric field, we want it set so that it deflects the beam in the direction opposite to the direction of bend by the magnetic field. Have the instructor inspect your reconfigured setup before turning any power back on. Now you are going to measure e/ m by balancing the electric field with the magnetic field. 1. Connect Pg to Fica (Fig. 11.4). Set Vps to 2000 V. 2. Supply current to the Helmholtz coil and adjust the current to get a straight line. (The B field should act opposite to the E field. Reverse the coil current if necessary) Adjust the current in the coils until the beam is as straight as possible though it will not be a perfect straight line. This can be attributed to the small plates and small coils: The electric and magnetic fields are not really constant, but vary near the edges of the apparatus. To get your best results in this part, you should seek a level beam near the center of the graticule, even if it is a few millimeters below (or above) the centerline. Since the beam does curve, first one way, then the other, try to make the tangent to the path level as your criterion. 3. Once a level tangent is achieved, record your values for Vps and I.