Physics 241 Lab: Cathode Ray Tube http://bohr.physics.arizona.edu/~leone/ua/ua_spring_2010/phys241lab.html NAME: Section 1: 1.1. A cathode ray tube works by boiling electrons off a cathode heating element and accelerating them with a large voltage difference. Then the high-speed electrons pass between a pair of charged deflection plates so that the path of the electron is altered. Finally, the electrons strike a screen coated with a fluorescent material and you see a scintillation take place (i.e. you see light emitted). All of this is done in a vacuum so that the electron can travel through the CRT unhindered by collisions with air molecules. Actually, there are two pairs of deflection plates: a pair of charged deflection plates for vertical deflection and another pair of charged deflection plates for horizontal deflection. (See figure.) Three-dimensional figure showing the operation of the CRT. The dotted line shows the path traversed by an example electron. 1.2. In the cathode ray tube, an electron is initially at rest (approximately) and is accelerated by a force produced by an electric field. However, in lab you will only know the positive change in voltage (really Δ ) of the plates through which the electron is accelerated. What simple formula using, q and W can you write to relate the work done on the electron to the change in voltage of the apparatus? Be careful, the charge of an electron is e. (Be sure to check your answer with other students or your TA) Your formula: Now plug in q = -e into your formula (for an electron):
1.3. Now slightly extend this formula using the work-energy theorem. The work-energy theorem states that the change in kinetic energy is equal to the work done on the object. Using this concept, write a formula relating the change in the electron s kinetic energy to the accelerating voltage of the apparatus (use, e and ΔK). (Be sure to check your answer with other students or your TA) Your formula: 1.4. Write a formula that describes the final velocity of the electron if it starts from rest and you know the work done on the electron (use v f, m e,, and e). (Be sure to check your answer with other students or your TA) Your formula: 1.5. Explain what the sign of the accelerating voltage difference must be in order for your formula in #3 to make sense? Reconcile this with your knowledge of how negatively charged particles respond to an electric field. Your explanation: 1.6. Now try out your formula using some numerical values. If the electron starts at the position x=0 on the following graph, find out the speed of the electron once it has reached the area of constant electric potential. (Remember that electrons flow upward in the voltage landscape.) You should use the electron charge, e = 1.6x10-19 C, and the electron mass, m e = 9.1x10-31 kg. Your calculations and answer in SI units:
Section 2: Now you know how to find speed of the electrons after they are initially accelerated, you will study how the electrons are deflected by the charged deflecting plates. 2.1. There are three electric fields affecting the trajectory of the electron. E a accelerates the electron initially to a high speed. E d,v causes a deflection in the vertical direction and E d,h causes a deflection in the horizontal direction. In the CRT figure below, draw arrows correctly depicting the direction and magnitudes of these fields. Do you best to draw E d,v in the three-dimensional picture. 2.2. Now examine a pair of charged deflection plates (see figure). The voltage difference between the plates is d,y. Assume the plates are separated by a distance d. Assume d,y is positive Find the magnitude and direction of the electric field between the plates E y in terms of d and d,y (ignore any edge effects). Your answer: Determine the acceleration a y felt by an electron inside the space between the plates using e, m e and E y. Your answer:
2.3. Now examine what happens when an electron enters the space between the vertical deflection plates (see figure). If the electron enters with a velocity in the x-direction of and travels the length of the plates w, how long does it take for the electron to reach the other side, Δt? Write your answer for Δt using w and. Your work and answer: Explain why this time Δt is not affected by the acceleration in the y-direction caused by the deflection plates? Your explanation: 2.4. As the electron traverses the space between the deflection plates, it is accelerated in the y- direction. Using the kinematics equation Δy = ½ a y (Δt) 2 to find vertical displacement Δy of the electron once it has reached the other side of the deflection plates. Write your answer for Δy using w,, e, m e and E y. Your work and answer in SI units: Use the kinematics equation v f,y = a y (Δt) to determine the final y-velocity v f,y when the electron has reached the other side of the deflection plates. Write your answer for v f,y using w,, e, m e and E y. Your work and answer:
Section 3: This section is not a problem, but you must read through it in lab. This is where all the analysis you have done from the previous section is synthesized together to derive the cathode ray tube equation. You will need to understand the following work in order to write your lab report. The derivation will use the following figure to find D y. 3.1. READ THE FOLLOWING SENTENCE TWICE Our goal here is to derive a final equation that relates D y to the only things we can control in the lab and d,y (as well as the things we can t control: the geometric parameters of the CRT d, w and L). Note that capital will always represent a voltage while a lower case v will always represent a velocity. In the derivation ignore directional 1 negative signs for simplicity, and also we need to use 2 m v 2 e o,x = e " (usually to substitute for ). First we need to find Δy: (You will need to justify each step below in your report.) ( ) 2 "y = 1 2 a y "t = 1 $ e # E y ' $ w ' & )& ) 2 % m e (% ( $ $ = 1 e '' $ d,y & & ))& & % d ()& w 2 2 & m e )& $ 2e # & )&& % (%% m e = 1 4 2 e # d,y # w 2 # m e = w 2 4d d,y d # m e # e # ' ) ) ') )) ((
Next we need to find Δy : (You will need to justify each step below in your report.) "y'= v f,y "t' # L & = ( a y "t)% ( $ ' # = % e ) E ) $ m e w &# L & (% ( ' $ ' # # e & d,y % % ( $ d ' = % ) % m e % $ = w ) L ) e ) d,y 2 d ) m e & ( w # ( L & % ( ( $ ' ( ' = w ) L ) e ) d,y 2d ) e ) = w ) L 2d ) d,y Finally this gives our equation for the total deflection on the oscilloscope screen D y : # D y = w 2 4d + w " L & % (" d,y. However, we cannot open up the CRT to measure d, w or L so we might as $ 2d ' well replace all these geometric factors with a single unknown geometric constant k : D y d,y. THIS IS OUR FINAL CRT DEFLECTION EQUATION. Note that by symmetry we get the same derivation for the total deflection in the horizontal z-direction: D z d,z g,z. THEREFORE, THERE IS A CRT DEFLECTION EQUATION FOR EACH DEFLECTION DIRECTION EACH WITH ITS OWN GEOMETRIC CONSTANT. Section 4: Now you need to answer some questions about the CRT deflection equations. 4.1. Given the CRT deflection equation in the vertical direction D y d,y, what you would see on the CRT screen if the deflection voltage was increased. Explain why this would happen using a physical argument (i.e. not using math). Your answer and explanation:
4.2. Given the CRT deflection equation in the vertical direction D y d,y, what you would see on the CRT screen if the accelerating voltage was increased. Explain why this would happen using a physical argument (i.e. not using math). Your answer and explanation: 4.3. You will now experimentally test the horizontal CRT deflection equation adjusting d,z and observing D z. D z g,z d,z by Use tape on screen to mark position of electron beam when there is NO DEFLECTION ( d,z set to zero to find the origin of the CRT). Be sure to record a and keep this value constant for the rest of this section. ( is the sum of B and C on the CRT power module and should be set as high as possible while the scintillation dot is still in focus). Record your constant accelerating voltage : Adjust d,z on the horizontal plates and mark D z on the tape for several values of d,z (make a data table with at least 5 data points). Record your data table of d,z and D z : Create graph of D z vs d,z by hand. Graph D z vs d,z on graph paper. Your data should give you a straight line. Measure the slope of the line of best fit. Since to obtain k g,z. Record your result for k g,z here in SI units: D z d,z g,z, the slope will equal k g,z so multiply by
4.4. You will now experimentally test the vertical CRT deflection equation D y d,y Use tape on screen to mark position of electron beam when there is NO DEFLECTION ( d,y set to zero to find the origin of the CRT). Be sure to record and keep this value constant for the rest of this section. ( is the sum of B and C on the CRT power module and should be set as high as possible while the scintillation dot is still in focus). Record your constant accelerating voltage: that you have derived by adjusting d,y and observing D y. This is because the geometry of the deflecting plates is different in the z-direction from the y-direction. Adjust d,y on the horizontal plates and mark D y on the tape for several values of d,y (make a data table with at least 5 data points). Record your data table of d,y and D y : Create graph of D y vs d,y by hand. Graph D y vs d,y on graph paper. Your data should give you a straight line. Measure the slope of the line of best fit. Since to obtain k. Record your result for k here in SI units: D y d,y, the slope will equal k so multiply by 4.5. You will now experimentally test in another way the horizontal CRT deflection equation D z g,z d,z by adjusting and observing D z. Set to about ½ to ¾ its maximum value and adjust d,z to the largest value possible that still enables you to see the scintillation dot (it may be fuzzy, but you should measure deflections using the center of the dot). Be sure to record d,z and to keep this value constant for the remainder of this section. Record your constant deflecting voltage d,z : Adjust to larger and larger values and record the corresponding horizontal screen displacement D z for several values of (make a data table with at least 5 data points). Record your data table of and D z : Linearize your data by making a graph of D z vs 1/ by hand. Graph D z vs 1/ on graph paper. Your data should give you a straight line. Measure the slope of the line of best fit. Since d,z to obtain k g,z. Record your result for k g,z here in SI units. D z d,z g,z, the slope will equal k g,z d,z so divide by
r Section 5: The magnetic force is given by F M = qv r " B r, but usually the speed of the charged particle is too slow to be able to visually see the effects of the magnetic force. However, electrons in CRTs move so fast, you can actually see them being deflected by a magnetic field. In fact, this is how oldfashioned television first worked. You must correctly predict whether the scintillation dot will be deflected horizontally or vertically when a magnetic field is created nearby the CRT. Then check your prediction. For this you will need to remember r what the cross product means in the Lorenz force equation (better ask around if you don t ), F M = qv r " B r and how to use the right-hand rule. Circle your predictions then check them experimentally: Report Guidelines: Title A catchy title worth zero points so make it fun. Goals Write a 3-4 sentence paragraph stating the experimental goals of the lab. [~1-point] Concepts & Equations [~6-points] Be sure to write a separate paragraph to explain each of the following concepts. Describe (without math) using text and diagrams how a cathode ray tube works. Examine the vertical CRT deflection equation. Explain how the deflection equation works (how to think about this equation). What happens to the deflection distance when d,y is increased and WHY? What happens to the deflection distance when is increased and WHY? Derive the deflection equation. Explain every step of the derivation from section 3. This is the largest part of this weeks report and will be worth a large percentage of the report grade. It should take at least a full page. You may leave spaces and write equations by hand, use equation editor or any other tool, but all the equations must be embedded into your report. Making notes of where to leave spaces in your report and keeping track of the equations that go into those spaces and later adding them by hand is probably easiest. Procedure & Results Write a 2-4 sentence paragraph for each section of the lab describing what you did and what you found. Save any interpretation of your results for the conclusion. [~4-points] Conclusion Write at least three paragraphs where you analyze and interpret the results you observed or measured based upon your previous discussion of concepts and equations. It is all right to sound repetitive since it is important to get your scientific points across to your reader. Do NOT write personal statements or feelings about the learning process (keep it scientific). [~4-points] Graphs All graphs must be neatly hand-drawn during class, fill an entire sheet of graph paper, include a title, labeled axes, units on the axes, and the calculated line of best fit if applicable. [~5-points] o The three graphs from section 4. Worksheet thoroughly completed in class and signed by your TA. [~5-points.]