Lab 12 em Experiment (Formal Lab #2)

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Moorpark College *

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M20

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Electrical Engineering

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Jan 9, 2024

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e/m EXPERIMENT Theory In order to measure e/m, the charge to mass ratio of the electron, a beam of electrons is accelerated through a known potential in order to determine the velocity of the electrons. The electrons are deflected by Helmholtz Coils and exhibit cyclotron motion. Prior to the class meeting, use the following equations to derive the equation for 5.3 2 i _ ZV(Z) a m (NuIr) Fm = qfixE where F’m= the magnetic force acting on a charged particle, g=charge on the particle, v =velocity, and B =magnetic field,. eV =—mv? and (5)%a for the Helmholtz Coils. where a=the radius of the Helmholtz coils (0.15m) N=the number of the turns on each Helmholtz coil (130 turns) T -m U,= permeability constant=4mx10~ T I=the current through the Helmholtz coils r=the radius of the electron beam path 72
Operation Measuring e/m Current adjust knob for Helmholtz coils Toggle Switch: Up for e/m experiment, Focus knob Down when using deflection plates. N + + Upper + - _ Lower| _ ®— ® 0|® © DC [ ] A(rg_r;i?r Voltmeter Power Supply = + (0-300 (Heater _VDC) 6.3 VDC or + |- | VAC) E— Power Supply ' (Helmholtz =l = Coils 6-9 VDC, Power Supply ripple < 1%) (Accelerating Voltage 150-300 VDC) Figure 4 Connections for e/m Experiment 73
e/m - The Charge to Mass Ratio of an Electron Procedure: 1. Place hood over e/m apparatus. 2. Flip switch to e/m measure position. 3. Turn off Helmholtz current power supply (on the left in the picture) 4. Place the power supply voltage adjust knob for the Helmholtz coils to the middle position. 5. Connect power supplies and meters to the e/m apparatus as shown in Figure 2 above. 6. Set the power supplies to the following levels: Electron gun: Set Heater: 6 VAC (CAUTION, DO NOT EXCEED 6V) The accelerating voltages will be 200V, 250V, 300V DC 74
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Vary the Helmholtz Coil Currents using the Helmholtz current power supply. Set the voltage control to the middle position and the current control to minimum. Vary the current by adjusting the current control knob. Watch the current meter and do not exceed 2 Amps. Vary the Helmholtz current 3 times for each accelerating voltage such that you get a well-defined circle that can be measured with the mirrored scale. 7. When the electron beam to emerges from the electron gun, make sure the plane of the electron beam circle is parallel to the Helmholtz coils (if not, turn the tube slightly until it is). 8. Read the current to the Helmholtz coils from the ammeter and the accelerating voltage from the voltmeter. 9. Measure the radius of the electron beam using the mirrored scale. Close one eye and move you’re your head left or right to align the reflected beam with the electron beam to avoid parallax errors. Measure the inside and outside radius of the beam on both the left and the right sides of the scales. Data: Errorin V: 6V = Errorinr: r = Errorinl: I = Accelerating Fleft Fright Helmholtz Voltage V Current 200V linside = linside = 200V linside = linside = 200V linside = linside = 250V Finside = Finside = 250V linside = linside = 250V linside = linside = 300V linside = linside = 300V linside = linside = 300V linside = linside = 75
ANALYSIS and DISCUSSION: Copy all of your data into and EXCEL spreadsheet and program a column to calculate the value of r which will be the average of Fieft and Fright for both Finside and Noutside for a fixed accelerating voltage and helmholts current. Program the e/m equation in the last column (you should have 18 rows of data in your spreadsheet). Print the program in the analysis section of your report. Use EXCEL functions (AVERAGE; STDEV) to calculate and average and standard deviation. Determine the percent discrepancyéof e/m. Use charge e = 1.60217646 x 10™" coulombs and electron mass = 9.10938188 x 10 kilograms. Note: percent discrepancy = experimental value—accepted value converted to %. accepted value \ . Standard dev. One way to get a predicted % error is converted to %. ylog average Another way to get a predicted error is to use differential error propagation. See the handout on error propagation. If this method is requested by your instructor, show all of the details of your error propagation in the analysis section and use equation editor for the algebra. Note if the percent discrepancy is less than the predicted error. (i.e. are your results within the margin of error?) Report: Write a formal report for this lab unless told otherwise by your instructor. 76