Electric Deflection Lab (Ch 5) PDF

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for general physics lab 2 and college physics lab 2...

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Measuring Electric Deflection with a Cathode-Ray Tube Lab Objective: To examine the qualitative and quantitative effects of electric fringe in a parallel plate capacitor by measuring the electron deflection produced when connected to an electrically charged cathode-ray tube (CRT). To quantify the effects of electric fringe, the effective length (leff) was first determined to measure the length (l) that the parallel plates would have to be in order to have deflection (d) without any fringing effects. The leff was then compared to the length of the plates in the CRT used to determine the strength of the fringing effects on a parallel plate capacitor. Theory: Cathode-ray tubes (CRT) in essence is a glass vacuum tube containing the components of a parallel plate capacitor and other electrical machinery designed to manipulate the movement of an electron at different electrical charges (V). The parallel plate capacitor is two metal plates that are equal in size but opposite in charge. The electric field exists only between the plates with equally spaced electric field lines flowing from the positive charge and terminating at the negative charge. The electric force extends from each plate in opposing directions due to the difference in charge, creating a repulsion between the plates equal in magnitude. Electric deflection is a process that begins with plugging in the power source to the electrical outlet. Once connected to an electric source, the electric charge will flow from the positively charged electrode from the anode to the negatively charged electrode leading to the cathode. This flow of electrons generates an electric potential from the electron gun (Vg), which will cause the electrons to flow into the CRT and heat the filament. This heat is converted to kinetic energy (KE) which will accelerate a negatively charged electron towards the positively charged metal plates, which demonstrates that the electrons follow the conservation of energy law. The electron in theory has low potential energy and accelerates towards the high potential energy plates charged at 600V. Electrons pass through a small hole called the electron gun to control the electron flow so that they pass individually through the deflection plates. The vacuum of the CRT makes air resistance negligible allowing the flow of electrons to accelerate according to Newton’s Second Law of Motion and two-dimensional kinematics generating a horizontal velocity that follows the x-axis, termed beam axis, and a linear velocity that is generated by the acceleration between the plates. The electron itself does not experience acceleration and only

follows the force created by the charge of an electric field, which is why the deflection path shifts upward towards the positive charge which means it is experiencing fringing effects. Once the electron passes through the plates, it will continue to move upward towards the positive charge of the phosphor screen. The phosphor screen itself is important because it contains charge, and once the electron hits the screen, a proton will be released, generating immunofluorescence which is the green light observed. Deflection appears as a line on the screen rather than a point due to the alternating charge produced by the AC voltage. This constant alternation between voltage means that the acceleration of the electron follows a sinusoidal pattern of motion, which is why we have to take the peak values of the deflection charge. The alternating charge also causes the electron to deflect in a back and forth motion similar to that of the sinusoidal curve, termed “sweep AC” which results in the deflection appearing as a line on the screen rather than a single point.

Figure 1: Theoretical model of electron deflection from the power supply to the cathode ray tube. Formulas: Vpeak=√ 2⋅ Vd❑RMS Equation 1: Calculate Vpeak from the multimeter RMS readings

Equation 2: Calculate the deflection of the parallel plates leff l ( +L) Vg⋅ s 2 Equation 3: Equation for slope of Figure 3 m=

2 d=(

Vd l 1 )( )( + L) Vg s 2

1 m) l +L 2 Equation 4: Calculate the efficient length of the deflector plates leff =Vg ⋅ s(

leff l Equation 5: Calculate the strength of the fringing effect. α=

Procedure: 1. Plug in power supply to outlet and wait 15 seconds 2. Set up the voltmeter to multimeter configuration to measure DC voltage 3. After 15 seconds, plug in the multimeter to the power supply 4. Set up the power box to DC configuration(+red wire to the -HC cathode plug) and measure Vg 5. Wait 15 seconds then unplug multimeter 6. Reconfigure the power box to AC configuration (+red wire to the sweep AC plug) and measure Vd 7. Use the knobs on the power supply to measure adjust the voltage to 10V, then using the caliper, measure the deflection on the screen in mm and record values. Then record the Vd values from the multimeter. 8. Repeat step 7 for 20V, 30V, 40V, and 50V 9. Using Equation 1 calculate Vpeak and it's error from the Vd values for each voltage. 10. Using Equation 2 calculate 2d and it's error from the d values for each voltage. 11. Record calculated values on table 2. 12. Use the program SciDavis to graph the the plates electron deflection (2d) as the y-axis and the peak deflection voltage (Vp) as the x-value to obtain the slope (m). 13. Using Equation 4 calculate the effective length 14. Using Equation 5 calculate the strength of the fringing effect. Data: Experimental values: Vg=583V±δ0.05V DC=5.07 —> s=5.23 mm —> l= 1.31 cm = 13.1 mm —> L= 5.70 cm = 57.0 mm

Table 2: The experimental calculations using Equation 1 & 2 with errors. Graphs: Figure 3: The linear fit of the deflection of the parallel plates (2d in mm) graphed as a function of the peak voltage deflection (Vpeak in V) (Slope: m=0.54 ±δ0.0001)

Calculations:

Questions: 1. Compare leff to l. Which is larger? Explain. Leff is larger than l because we are calculating the length the plates would have to be so that the deflection could be explained without the fringing effect, so leff would have to be greater than l. 2. Newton’s kinematics break down when traveling near the speed of light. Compare the speed of an electron in the cathode-ray tube calculated from Eq. (5.9) to the speed of light c = 3 *108 m/s. Are relativistic corrections necessary? Note: Relativistic effects become important at around 50% of the speed of light. No further calculations are necessary because the velocity calculated for the CRT is greater than the speed of light. 3. In case the experiment in Ch. 4 was already conducted, compare the results for a. Calculate how well the measurements agree. Which measurement is more precise and why? The alpha value in ch 4 was 1.045, compared to the alpha for ch 5, 0.337. But alpha wasn't calculated for that experiment...