Lab 1_ Charge to Mass Ratio of the Electron

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Feb 20, 2024

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Charge to Mass Ratio of the Electron Bassel Marouni & Joannie Naluz PCS 130 - Physics II Section 10 Vladislav Toronov Fatemeh Lalegani Dezaki

Introduction A magnetic field is when the surrounding space of a magnet is affected and magnetism is observed. Uncharged particles do not create a magnetic field, but charged particles do when they are in motion. Depending on the particle's charge, the magnetic field could have different properties. The charge-to-mass ratio is the charge divided by the mass of a particle, and so different particles each have their unique charge-to-mass ratio. That means that scientists could use the charge-to-mass ratio to identify whether a particle is an electron or a proton. The main objective of this experiment is to calculate the charge-to-mass ratio of the particle with the equipment listed below. This will be determined by collecting the motion of the particle in the magnetic field at different radii and currents. Procedure This experiment was conducted using an e/m apparatus; composed of an e/m tube, Helmholtz coils, a high voltage power supply, a low voltage variable power supply, banana cables, a wooden cover, and a meter stick. The power supply was turned on, and the voltage was set to 230V and left running until a circular, green beam formed. While maintaining the voltage, the current was changed which simultaneously changes the diameter of the circle, both these values were collected. This process was repeated until ten trials of different diameters were conducted, and these values are shown in Table 1. A scatter plot was created to compare the variables of the coil current versus the radius of the beam, and a line of best fit was created. Results and Calculations The diameter displayed through each change of current was observed by looking at the measuring stick inside the e/m apparatus ( Table 1) . The r 2 was dividing the diameter by 2, and then squaring it as shown below, 2 = 7.56 x 10 (-4) m 2 ( 0.055𝑚 2 ) 2 = 7. 5625𝑥10 (−4) 𝑚 The magnetic field, B, was determined by using the equation, 8µ𝑁𝐼 𝑎 125 Where μ 0 is 4π x 10 -7 (resistance around a magnetic field), N is 130 (number of coil turns), I is the current (in Amperes), and a is 0.1525 (the average radius of every coil). A sample calculation for the first trial is shown below, = = = 1.76 x 10 -3 T 8µ𝑁𝐼 𝑎 125 8𝑥(4π 𝑥 10 −7 )𝑥130𝑥2.30 𝑎 125 3.005873312𝑥10 −3 1.705001833 Ten trials were performed and data was collected, this can be seen in Table 1.1 .

Current (A) Diameter (m) r 2 (m 2 ) B (T) 1 𝐵 2 2.30 0.055 7. 5625𝑥10 −4 1.76769 x 10 -3 321742.4433 2.18 0.059 8.7025 x 10 -4 1.67546564 x 10 -3 358138.5247 2.11 0.060 9.00 x 10 -4 1.621666292 x 10 -3 382295.4392 1.97 0.065 1.05625 x 10 -3 1.514067581 x 10 -3 438562.5821 1.86 0.070 1.225 x 10 -3 1.429525736 x 10 -3 491969.4545 1.73 0.075 1.40625 x 10 -3 1.320612647 x 10 -3 568685.0629 1.63 0.080 1.60 x 10 -3 1.252756425 x 10 -3 640602.7795 1.55 0.085 1.80625 x 10 -3 1.152843335 x 10 -3 708436.0145 1.46 0.090 2.025 x 10 -3 1.122100847 x 10 -3 798469.4712 1.31 0.095 2.25625 x 10 -3 1.006816513 x 10 -3 991793.9076 Table 1 - Data Collected on Particle’s Properties as Current Change s It was observed that as the current and the radius were inversely proportional, meaning that as the current increased, the radius of the beam decreased. This was the major tell that the observed particle was not a proton, since proton current and proton radius are proportional. For a proton, if the current was increased, then the radius of the beam would increase with it as well.

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