PCS125-Lab-5-Daniel--Afrah.docx

Department of Physics Course number 125 Course Title PCS125 Semester/Year 2021-2022 Instructor Aidan Brown TA Name Zachary Anstey Lab/Tutorial Report No. 5 Report Title Charge to Mass Ratio of the electron Section No. 34 Group No. 123 Submission Date 2022-03-28 Due Date 2022-03-28 Student Name Student ID Signature Daniel Spahn-Vieira 501102103 DRSV Afrah Chishty 501027994 AC

Introduction: The objective of this lab is to observe the behaviour of a charged particle traveling in a uniform magnetic field. We will perform various experiments to confirm that the particle's velocity will travel in a circular path, and that the magnetic field is perpendicular to the velocity. Additionally using observations of how the path of the electron changes with respect to the changing magnetic field intensity, the charge/mass ratio of an electron will be determined. Theory: This lab utilized both magnetic and electric fields to put electrons into uniform circular motion, from which the charge/mass ratio of the electron could be determined. In this experiment, electrons were accelerated to high velocities using strong electric fields. Once the electrons were in motion their trajectories were shaped using strong magnetic fields, so that the electrons moved in uniform circular motion. It is known centripetal force causes acceleration toward the center of a circle, in this experiment, the magnetic fields emanating perpendicular to the helmholtz coils, thus applying a magnetic force perpendicular to the electrons path of motion, thus curving its path into a circle with a variable radius depending on the current through the coil. The formula for centripetal force is given as follows: F c = mv 2 /r The velocity of the electrons “boiling” off the filament was increased by accelerating them through a potential difference. In essence the change in potential energy was equal to the change in kinetic energy. ΔU+ΔK=0 K=1/2mv 2 U=ΔV U B -U A =q(V B -V A ) Finally the electrons were subjected to a magnetic force acting perpendicular to their initial motion. The magnitude of the magnetic field intensity varied with respect to the current running through the helmholtz coils and could be determined as follows: Based on all of the above relationships, the charge mass ratio can be determined using the following formula:

Results and Calculations: Table 1.0: Radius vs. Amperage voltage: 308 V radius (m) current (A) uncertainty (δ) 0.05 2.76 0.244444 0.055 2.54 0.174874 0.06 2.34 0.111628 0.065 2.18 0.061032 0.07 2.04 0.01676 0.075 1.9 0.027512 0.08 1.8 0.059135 0.085 1.7 0.090757 0.09 1.6 0.12238 0.095 1.54 0.141354 0.1 1.46 0.166652 Table 2.0: Magnetic field vs Radius Magnetic Field (1/B^2) Radius (r^2) 245949.2204 0.0025 290399.7118 0.003025 342162.0975 0.0036 394230.8688 0.004225 450197.7078 0.0049 518986.9199 0.005625 578253.9447 0.0064 648284.6993 0.007225 731852.6488 0.0081 789991.0529 0.009025 878937.3151 0.01

Graph 1.0: Magnetic Field vs Radius plot Analysis 1) 2)

the lab (r=0.05m I=2.76A) it can be seen that 95 928 143.71=2(308)/(0.00216 2 r 2 ). Solving for r, it is determined that the radius at this current and voltage is 0.727m for a proton, whereas the experimental data has a radius of 0.05m thus the claim can be made that this particle is not a proton. 4. Knowing that c/m=2V acc /B 2 r 2 and that the values for V 1 and V 2 are 250V and 400V respectively and that the initial radius is 0.03m it can be determined that 1=(500/B 2 r 1 2 )/(800/B 2 r 2 2 ) thus (r 1 2 /r 2 2 )=⅝ thus the increase in voltage should increase the radius to 0.03(sqrt(⅝))= 0.038m. 5. Inconclusive data. Conclusion In this lab, the mass to charge ratio of an electron was determined experimentally, by observing the behaviour of electrons under the influence of strong electric and magnetic fields. by accelerating the electrons up to high velocities and then curving their trajectories using perpendicular magnetic fields. Once uniform circular motion was achieved, the radius of the motion was altered by a controlled change in current through the Helmholtz coil from which the magnetic fields were emanating, by observing the change in radius with respect to the change in current, the sensitivity of the electrons to magnetic field intensity could be determined. Using the formula e/m=2V acc /B 2 r 2 along with the formula for magnetic field intensity B=8µ 0 NI/a√125 , we were able to calculate their respective values to analyze for the confirmation of our theory. In the second part of our experiment, we bought a bar magnet close to the electron beam. We observed deflection, and after playing around with the apparatus, we concluded that the lower the current, the more deflection was shown from the bar magnet. In the first part of our lab, we turned the knob and recorded currents with different associated diameters. The smallest diameter yielded an amperage of 2.76. Using the plotted radius vs magnetic field (Graph 1.0), we calculated e/m. we compared this to our theoretical value, and since we got a considerably low error (13%), we can conclude that our theory was confirmed, and that magnetic field is perpendicular to the velocity,

and because of the blue-green hue shown in a circular path, we can also confirm that the particle had a circular path. References Serway and Jewett, Physics for Scientists and Engineers with modern physics, 10th edition, Brooks Cole, Jan. 1 2018