PHY 112 Lab 3

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Rio Salado Community College *

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112

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Electrical Engineering

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Apr 3, 2024

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Michaela Blackmore #14371 2/18/2024 Lab 3: Equipotential Mapping Question: The purpose of this lab is to observe the electric potentials between a positive and a negative source at varying positions. This will be conducted by using a battery to create a potential difference between two points that will then be measured using a voltmeter. Using 2D and 3D graphs, the relationship between distance and potential differences will be observed. Materials: From lab kit: ● 9V battery ● 9V battery connector ● 2 insulated wires with alligator clips ● Voltmeter ● Styrofoam base ● 2 Nails Student provided: ● Flat-bottomed glass container ● Permanent marker ● Tape ● Tap water Procedures: A grid was created by measuring 1cmx1cm spaces on a piece of styrofoam. This grid was then labeled 1-8 and A-I. Two nails were then placed in spaces that were 6cm apart. The nails were inserted so that the head of the nail was on the unlabelled side of the grid and the point of the nail facing up out of the styrofoam. A mark was made directly in the middle of the two nails creating a zero potential location. Insulated wire was then connected to the tops of each nail using an alligator clip. The other end of the insulated wires were then connected to the leads on the 9V battery connector. The battery was left unconnected while the voltmeter was set up and set to 20DCV. The battery was then connected. The black voltmeter lead was placed in the water at the zero potential location, directly in the middle of the two nails. This lead remained at the same location throughout the experiment ensuring it is in the water and not pushing in the styrofoam. The red lead was then moved throughout the grid starting at the A1 grid space and measuring until all spaces A1- I8 were measured and recorded. A 2D and 3D contour graph was then created to visualize the location of the voltmeter to the electric potential generated.

Michaela Blackmore #14371 2/18/2024 Photos: Data: Table 1: Electric Potential Measured at Each Grid Space Nails were placed at C4 and G4. Values were measured in voltages (V).

Michaela Blackmore #14371 2/18/2024 Calculations and Graphs: Distance between nails= 6cm Graph 1: Graph 2:

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Michaela Blackmore #14371 2/18/2024 Results: Voltages measured in grid spaces A-D measured in the negative values, while grid spaces E-I had voltages in the positive values. The zero potential location is located directly in between the nails and is in grid space E5. Potential was at its most negative values when closer in proximity to the negative nail, while the most positive values were when the voltmeter was most near the positive nail. This is observed through the tables and graphs. In graph 1 the most positive voltages measured were the spaces in maroon. These were all grid spaces that encompassed the positive nail. The most negative voltages measured were the spaces in orange. These were all grid spaces that encompassed the negative nail. In graph 2, the same trends were observed by peaks and valleys. The peaks were surrounding the positive nail, observed in dark blue, and the valleys around the negative nail, observed in bright blue. Conclusions: In this lab, electric potentials between a positive and a negative source at varying positions were observed and measured. A battery was used to create potential differences between two points that were then measured using a voltmeter. Potential is dependent on the distance from the source charge and the amount of charge that is held by the source charge. These electric potentials are represented by the various voltages measured using the voltmeter at different positions, seen in table 1. A 2D and 3D graph was then generated to visualize the positions within the field to the voltages in each grid space. These graphs demonstrated equipotential lines within the system. The 3D graph represented positive voltages as hills, while negative voltages appeared as valleys. A uniform electric field, would have voltages that change consistently with equipotential lines that would be spaced evenly throughout, but in a nonuniform field the voltages would be observed to be higher as the meter is moved closer in proximity to the source. In this experiment, a nonuniform field was outlined. This is elucidated through Graph 2, the 2D graph. The orange outline represents voltages that are most negative and are most near the negatively charged source, while the maroon area on the opposite side of the grid represents the most positive values. The nails were placed in spaces C4 and G4. As the black lead of the voltmeter was closer to C4, negative, the voltages became more negative and as the voltmeter moved more towards G4, positive, the voltages became more positive. A zero potential location was determined to be in the middle of the nails and should have been measured at 0. In table 1, it is identified as slot E5. It would be expected that the most positive value would be 4.5V and the most negative value would be -4.5V. However, the most negative voltage measured was -2.91V and the most positive was 2.18V. This could have resulted from error. It was difficult to keep the control lead in the same exact spot while measuring the rest of the grid spaces. It is very possible that the lead moved or touched the styrofoam intermittently, which is why we do not see equal positive to negative values on opposing sides of the grid. Although the results still support the ideas being explored, it does not paint a perfect picture for what should have been observed. The voltmeter also read the battery as 9.2V when testing the setup, when it should have read at 9V exactly. This may have caused discrepancies in the values obtained. The zero potential location should have

Michaela Blackmore #14371 2/18/2024 read at 0V; however when completing the assignment the closest to 0V that was obtained was 0.05V, which also is a slight error in the experiment. If the values were as expected, it would have generated a clearer 3D graph with more prominent peaks and lower valleys. The 2D graph would have been more symmetrical where the most negative or positive values were measured. Ultimately the experiment went as close as possible to what was expected. To achieve the largest potential, a positive particle should be placed as close as possible to the positive nail and to achieve the most negative voltage it should be placed as close to the negative source. Analysis Questions Response: 1. At what grid position should you place a positive particle so that it has the largest potential? At what position would you place a negative particle? Explain. To achieve the largest potential, a positive particle should be placed as close as possible to the positive nail. This is because the like charges. Like-charges have a higher energy requirement so it will result in the largest potential. The same is for the negative particle. To achieve the largest negative potential, a negative particle would need to be placed nearest the negative nail. The closer the like charges then the increase in repulsion and the greater need of energy. 2. Describe how your results would change if you used a 12V car battery instead of a 9V battery. Be specific and explain your answers. If the voltage of the battery was 12V instead of 9V, then the potentials generated at each position would also increase. Greater peaks and valleys would be observed in each graph because the voltages would be either more negative near the negative nail or more positive near the positive nail than observed in the previous experiment. The 12V battery produces more energy potential throughout. 3. Describe how your results would change if you placed the black voltmeter lead at the negatively charged nail rather than at a point halfway between the two nails. Be specific and explain your answers. Placing the black voltmeter closer to the negative charged nail rather than halfway would change the zero potential location. Instead of being measured at 0.0 because it is directly in the middle, it would be slightly or mildly negative. For instance, instead of being in the middle, which was measured at grid space E5, if the black voltmeter was placed closer to the nail it would be more negative like observed by grid space D5. This is because the like charges are closer, creating a greater force of repelling each other. Changing the black voltmeter’s position would then skew all of the data to the left resulting in more

Michaela Blackmore #14371 2/18/2024 negative voltages generated due to smaller magnitudes and smaller electric potentials generated. 4. If you placed a particle with a charge of +4 μC at position D3 on your grid, how much electric potential energy would the particle have? Show your work. Did work occur on or by the particle to move the charge to this position? Explain your answer. V=Ue/q D3= -0.53V -0.53V= Ue (4x10^-6C) Ue= -2.12x10^-6J Ue represents the amount of energy required to move the particle to the D3 location. Work was done on the particle. It would require -2.12x10^-6J to move the particle to D3. References: Urone, P. P., & Hinrichs, R. (2012). 19.1 - Electric Potential Energy: Potential Difference. In College Physics. OpenStax. Urone, P. P., & Hinrichs, R. (2012). 19.2 - Electric Potential in a Uniform Electric Field. In College Physics. OpenStax. Urone, P. P., & Hinrichs, R. (2012). 19.3 - Electric Potential Due to a Point Charge. In College Physics. OpenStax

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