Wendler_K_152_lab4_

Karsyn Wendler Physics 152- Lab Section: Wednesday 2:00pm Lab #04- Magnetic Fields and JJ Thompsons E/M Experiment September 20, 2023 INTRODUCTION My lab partner Sophia and I explored polarity and magnetic fields today. We did this first at a small scale with magnets. Then using PASCO software, we attempted to analyze Earth’s magnetic field. We then theorized on how forces interact in magnetic fields, including how this is calculated and observed. Finally, after applying these lessons to the idea of charged particles moving in a magnetic field, we used a Helmholtz apparatus to measure aspects of current, voltage, shape/radius of electrons in electric fields. This data all culminated in the calculation and understanding of the value of e/m. PART ONE: MAGNETIC FIELD LINES 1-A, B & C We began by placing a magnet on a sheet of paper, tracing it’s outline and marking the north and south poles. Then, we used a compass to verify that the poles were marked correctly. The compass was then placed near the end of the magnet, and the point that the compass needle pointed to was marked with a dot. This dot was used as a guideline for the next compass movement as we lined up the other needle to the dot and marked the next one. We repeated this process a few more times as well as on the other side of the magnet, then connected the dots with a line and drew arrows in the direction in which the north end of the needle pointed. The full drawing can be seen below: Most of the field lines return to the other end of the magnet. Those at the far ends have a gap in their field lines since they travel a longer path to get back to the opposing end of the magnet. but the ones on the very end (perpendicular to the short width of the magnet) never seem

to come all the way back. This is likely because the field line goes through the pole and kind of ‘wraps around’ to the other side. 1-D We will take a second magnet, arrange and trace the two on the paper with opposing poles facing one another. The same compass arrow marking method from part 1-B was used to make note of the magnetic field lines between the two magnets. The results are seen below: 1-E & F Now, the two magnets are arranged so both north poles are facing each other. The same tracing and field marking method was used again for this analysis, and the results follow:

2-B We first tested the magnetic-field sensor by running it along the bar magnet from part 1. From the graph, we found that the north end of the magnet read as a negative magnetic field and the south end of the magnet read as a positive value magnetic field. The closer the probe was to the end of the magnet, the more extreme (either positive or negative) the value was. 2-C & 2-D We then used the probe to try to find the direction and magnitude of the magnetic field of Earth. We erased old data, TAREd the probe, and began collecting new data by holding the probe in different directions. We found the most positive graph values when the probe was straight down and the most negative values were graphed when straight up. With the relative data, we cleared the PASCO graph and started a new data collection. This is the resulting chart:

We averaged around the most positive and most negative values and used the following equation to attempt to solve for the value of the magnitude of Earth’s magnetic field: |࠵? #$%&’ | = )*࠵? +,-& /,-0&01# * + *࠵? +,-& 3#4$&01# *5 2 |࠵? #$%&’ | = (|. 35| + |−.31|) 2 |࠵? #$%&’ | = .33࠵? 2-E & 2-F & 2-G Based on our measurements, the angle of Earth’s magnetic field is perpendicular (90- degrees) with the north wall. That means it has a zero degree angle/ is parallel with the vertical. Because Earth’s tiled axis of rotation does not align with the Earth’s magnetic poles, we know that there is likely some sort of error in these measurements. We can likely blame it on the amount of electronics/metal objects throughout the physics laboratory altering the readings. Again, after looking at a diagram of Earth’s magnetic field and noting the latitude (34N) and longitude (118W), we can once again confirm that our data/readings are likely inaccurate. The angle should have been in the north western direction rather than just west. 2-H & 2-I Based on Wikipedia’s page on Earth’s magnetic field, the magnitude measurement for us in Los Angeles should have been closer to .47G rather than in the .30s. Based on diagrams from that same search page, the inclination angle in Los Angeles is around 60-degrees, and the declination angle is around 12-degrees. Once again, our measurements of 90-degrees and 0-degrees do not quite match up with these. This is likely due once again to the metal objects and structures throughout the building the laboratory was in, especially since it was at the basement level, leaving multiple levels of metal structure all around. PART THREE: FORCE ON A MOVING CHARGE 3-A Consider a charged particle in the x-y plane, ࠵?࠵?࠵?࠵?࠵? = ࠵? = 2.9 × 10 G ࠵?/࠵?, ࠵? = 30° with respect to the x axis. Magnetic field in the +y direction of strength 2.6 millitesla. ࠵? ⃗ = ࠵?࠵?⃗ × ࠵? P⃗ ࠵? ⃗ = ࠵? ⃗ × ࠵? P⃗ *࠵? ⃗ * = *࠵? ⃗ × ࠵? P⃗ * = *࠵? ⃗ **࠵? P⃗ *࠵?࠵?࠵?࠵? Magnitude and direction of the force exerted on the particle by the magnetic field? PROTON: ࠵? = +1.6 × 10 VWX ࠵? ࠵? ⃗ = (1.6 × 10 VWX )(2.9 × 10 G ) × (2.6 × 10 VY )࠵?࠵?࠵?30 ࠵? ⃗ = 6.03 × 10 VWG Direction= out of the page

5-A Using the right hand rule, we determined that the Lorentz force on the electron is in the downward direction. Because this force is acting in the downward direction, the electron will NOT still be travelling in the same horizontal straight line depicted, but start moving in a downward trajectory. 5-B Yes, the Lorentz force is perpendicular to the direction of motion of the electron in all moments (first, second, onward) because this force is the cross product of the velocity and the magnetic field and all cross products are perpendicular to their components. 5-C No work is done on the particle as it moves in a curved path. This is because force is perpendicular to direction of motion, so based on the rule of the dot product of the work done will be zero. Furthermore, because there is not any work done on particle, the speed stays the same. 5-D Displacement of electron bending in a magnetic field for the first three moments in time (black) and next 5 moments in time (red): 5-E If broken up into even more steps, the shape of the electron’s path would become a circle. Furthermore, if the magnitude of magnetic field B was increased, the path would still be a circle, but with a smaller radius as a greater force would be acting on it. 5-F In preparation for part 6, we used a compass to verify that the direction of the magnetic field between the current carrying Helmholtz coils is aligned with their axis. 5-G We combined the following equations: ࠵? ࠵? = ࠵? ࠵?࠵? ࠵? = [ 2࠵?࠵? ࠵?

࠵? = ࠵? ^7.8 × 10 Va ࠵?࠵?࠵?࠵?࠵? ࠵?࠵?࠵? e to solve for the ratio of e/m: ࠵? ࠵? = f 2࠵?࠵? ࠵? ࠵?(7.8 × 10 Va )࠵? and a formula for the radius r: ࠵? = ࠵?࠵? ࠵?࠵? ࠵? = f 2࠵?࠵? ࠵? ࠵? ࠵?(7.8 × 10 Va )࠵? PART SIX: MEASURING E/M FOR AN ELECTRON 6-A Finally, to measure the radius of the radius of the electron’s orbit in a magnetic field and deduce a value for the e/m ratio of the electron, we will set up our apparatus. To do this we connected two wire form the ‘6.3 VAC’ output on the Heath/Zenith power supple to the Power Supple Heater inputs on the e/m apparatus. Then, we connected two wires from the ‘B+ Volts’ output terminals of the Heat/zenith power supply to the ‘power supply accelerating voltage’ terminals of the e/m apparatus. Next, we connected two wires from the digital voltmeter (set to measure DC volts) to the ‘voltmeter’ terminals on the e/m apparatus. We set the VIZ power supply to a current limit of 2.0 amps maximum, then connected two wires from the VIZ supply output terminals to the ‘helmholtz coils’ input terminals on the e/m apparatus. Finally, with all wires connected properly, we were able to turn on all of the machines and observe the stream of electrons and their green hue in the apparatus. Now, we altered the accelerating voltage to watch how the beam path may change. We found that as we increased the accelerating voltage (B+), the circle’s radius increased, and when B+ was decreased, the radius got smaller. 6-B We then altered the current through the Helmholtz coils to see how the beam path changes with the magnetic field strength. As the magnetic field strength was increased, the radius decreased. Inversely, when the magnetic field strength decreased, the radius increased. This is logical based on the radius equation found in part 5 as it has the current on the bottom of the ratio indicating that a larger value I = smaller value r and vice versa. 6-C We used a ruler to take our best measurement of the radius of the circular beam path. We found it to be 2cm with a 1.61 current.

Experiment Review Questions: 1. B 2. D 3. A 4. C? 5. D 6. A 7. B? 8. B? 9. D? 10. B 11. A