Physics 241 Lab: Cathode Ray Tubehttp://bohr.physics.arizona.edu/~leone/ua_spring_2009/phys241lab.htmlName:____________________________“Geometry”I prove a theorem and the house expands:the windows jerk free to hover near the ceiling,the ceiling floats away with a sigh.As the walls clear themselves of everythingbut transparency, the scent of carnationsleaves with them. I am out in the openand above the windows have hinged into butterflies,sunlight glinting where they’ve intersected.They are going to some point true and unproven.-Rita DoveImportant:- In this course, every student has an equal opportunity to learn and chance of success.- How smart you are at physics depends on how hard you work. Work problems daily.- Form study groups and meet as often as possible.. - Join professional organizations. - Physicists help people: science => technology => jobs.For some of the following problems, you may find it helpful to refer to the diagram shown below toremind you how to relate the most common electrostatics concepts. Incidentally, you should bemaking similar formula sheets as you work homework problems.Section 1:1.1. A cathode ray tube works by ‘boiling’ electrons off a cathode heating element and acceleratingthem with a large voltage difference. Then the high-speed electrons pass between a pair of chargeddeflection plates so that the path of the electron is altered. Finally, the electrons strike a screen coatedwith a fluorescent material and you see a scintillation take place (i.e. you see light emitted). All of thisis done in a vacuum so that the electron can travel through the CRT unhindered by collisions with airmolecules. Actually, there are two pairs of deflection plates: a pair of charged deflection plates forvertical 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 aforce produced by an electric field. However, in lab you will only know the positive change in voltageVa (really “DVa”) of the plates through which the electron is accelerated. What simple formula usingVa, q and W can you write to relate the work done on the electron to the change in voltage of theapparatus? Be careful, the charge of an electron is –e. (Be sure to check your answer with otherstudents 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 theoremstates 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 Va of theapparatus (use Va, e and DK). (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 youknow the work done on the electron (use vf, me, Va, and e). (Be sure to check your answer with otherstudents or your TA!)Your formula: 1.5. Explain what the sign of the accelerating voltage difference Va must be in order for yourformula in #3 to make sense? Reconcile this with your knowledge of how negatively charged particlesrespond to an electric field. Your explanation:1.6. Now try out your formula using some numerical values. If the electron starts at the positionx=0 on the following graph, find out the speed of the electron once it has reached the area of constantelectric potential. (Remember that electrons flow upward in the voltage landscape.) You should usethe electron charge, e = 1.6x10-19 C, and the electron mass, me = 9.1x10-31 kg. Your calculations andanswer 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. Ea accelerates the electroninitially to a high speed. Ed,v causes a deflection in the vertical direction and Ed,h causes a deflection inthe horizontal direction. In the CRT figure below, draw arrows correctly depicting the directionand magnitudes of these fields. Do you best to draw Ed,v in the three-dimensional picture.2.2. Now examine a pair of charged deflection plates (see figure). The voltage difference betweenthe plates is Vd,y. Assume the plates are separated by a distance d. Assume Vd,y is positiveFind the magnitude and direction of the electric field between the plates Ey in terms of d and Vd,y(ignore any edge effects). Your answer:Determine the acceleration ay felt by an electron inside the space between the plates using e, me and Ey.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 vo,x and travels the length of the plates w, howlong does it take for the electron to reach the other side, Dt? Write your answer for Dt using w andvo,x. Your work and answer:Explain why this time Dt is not affected by the acceleration in the y-direction caused by the deflectionplates? 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 Dy = ½ ay(Dt)2 to find vertical displacement Dy of the electron once ithas reached the other side of the deflection plates. Write your answer for Dy using w, vo,x, e, me andEy. Your work and answer in SI units:Use the kinematics equation vf,y = ay(Dt) to determine the final y-velocity vf,y when the electron hasreached the other side of the deflection plates. Write your answer for vf,y using w, vo,x, e, me and Ey.Your work and answer:Section 3: This section is not a problem, but you must read through it in lab. This is where all theanalysis you have done from the previous section is synthesized together to derive the cathode raytube 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 Dy.3.1. READ THE FOLLOWING SENTENCE TWICE! Our goal here is to derive a final equationthat relates Dy to the only things we
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