PCS125-Lab-5-Daniel--Afrah

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Toronto Metropolitan University *

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125

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Physics

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Apr 3, 2024

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pdf

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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:

e/m=2V acc /B 2 r 2 Apparatus: - E/m Tube - Banana cables - Set of Helmholtz coils - Bar Magnet - High voltage power supply - Wooden cover - Low voltage variable power supply Procedure: Make sure at the start of the lab that all the coils are parallel to the earth’s magnetic field, the box and wires should all be connected and set up properly in advance. Consult the TA otherwise. Make sure all the power supplies are off, notice the two knobs for voltage and current. Turn on the power supply, and increase the voltage until it reaches 200-400 V or until you see a distinguishable blue-green beam emanating from the anode. Bring a magnet close to the beam, and record your observations, regarding deflection. Increase the current slowly, and notice the circular path appearing inside the tube. Change the radius of the curvature of the electron beam by adjusting the current, note the current required to make the smallest diameter. Repeat these steps for at least 10 unique diameters. Turn off all power supplies and adjust knobs to 0.

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