Physics 2 Lab 4

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Massachusetts Institute of Technology *

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8.02

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Electrical Engineering

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Oct 30, 2023

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Electric Potential and Electric Field Lab Number and Title: 203 Electric Potential and Electric Field Name: Aaron Hsu Group ID: N/A Date of Experiment: 10/11/22 Date of Submission: 10/18/22 Course and Section Number: PHYS 121A013 Instructor’s Name: Matias Daniel de Almeida Partner’s Names: Paul Svorec, Alex Ack, and Noah Francois 1. Introduction: The goals and objectives of this lab are to calculate the electric potential and the electric field from three different charge setups by using MATLAB. Draw the electric field and field lines along with drawing a contour and surface plots of the electric potential. For the three different charge setups, experimentally measure the electric potential and locate the equipotential lines and draw the electric field lines. For the two line charge setup, experimentally calculate the electric field by the actual measured electric potential and plotting the graph of electric potential vs. position. With electrostatic forcing being a conservative force along with potential energy being involved in other conservative forces and when working with electrostatics, the idea of electric potential energy and electric potential which is known as the electric potential energy per unit charge also comes up. Electric potential is a scalar quantity within an electric field at any point, which helps to explain electrostatics easier and better than vectors like electric forces and electric fields. Electric potential in a system of point charges is equal to the sum of the point charges’ individual potentials due to the scalar nature of the electric potential. Electric potential can be measured using a voltmeter and using a ruler we can measure the position. Electric field can be found by measuring the electric potential at several different positions in the field and creating a graph of V versus position where the slope of the graph is the electric field component at the related position. The equations, and show that the electric 𝐸 ? =− ∂𝑉 ∂? = 𝑉(?+∆?,?)−𝑉(?,?) ∆? 𝐸 ? =− ∂𝑉 ∂? = 𝑉(?,?+∆?)−𝑉(?,?) ∆? field lines have to always be perpendicular to the equipotential lines. This shows how the electric field and the lines are drawn once equipotential lines are found. We are going to

be looking at two point charges separated by a distance, one point charge and one uniform line charge separated by a distance, and two parallel uniform line charges. We will use MATLAB in order to theoretically calculate the electric potential and electric field as a function and the electric field lines will also be drawn and displayed. Experimentally, we will use a voltmeter to find the equipotential lines and then draw the electric field lines. For two parallel uniform line charges, we will also manually calculate the electric field by the actual measured electric potential and plotting the graph of V versus position and then compare experimental measurements with theoretical calculations. 2. Experimental Procedure: The equipment for this lab are red and black leads, three field plates including two-points, MATLAB, u-shaped probe (wand), flexible curve, electric field mapping apparatus consisting of a field mapping board, a voltmeter, parallel plate and point-plate templates and two plastic templates, graph papers, and a dc power supply. We followed the same experimental procedure that is written in the lab manual. We used MATLAB to compute the electric potential and plotting contour, surface, and vector field plots for the three different charge configurations. To set up the experiment we first turned over the field mapping board and unscrewed the thumb screw from each metal bar and would choose the corresponding plate for the charge configuration and have the black part of the plate face upwards and screw it in underneath the field mapping board. We then would attach a sheet of graph paper to the top of the board. Then we would choose the correct design template for the charge configuration so that it lines up with the plate that is underneath the board and then trace the design onto the graph paper. Then we would connect the voltmeter and the u-shaped probe and use the u-shaped probe on the board to find equal voltages and mark it on the graph paper and then connect them using the flexible curve. We would then repeat this to find equipotential points for other voltages and repeat it for the other configurations. 3. Results: * q 1 q 2 q 3 q 4 q 5

Point Charge (V) 2.5 3.0 2.0 1.0 4.0 Line Charge (V) 2.0 3.0 1.0 0.5 4.0 Point & Line Charge (V) 2.0 3.0 1.0 4.0 0.5 *all values are approximate Two point charge configuration: Point-line charge configuration:

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Two parallel-line charge configuration:

4. Analysis and Discussion: It is not possible for two different equipotential lines or two electric force lines to cross because electric field lines cannot cross as well. Also, since they have different electric potential values to be different and separate lines, and in any point along the electric field there would be only one constant electric potential value for a configuration of charges which also results in it not being possible for two different equipotential lines or two electric force lines to cross. Lines of electric force must be at right angles to equipotential lines because along the electric field, electric potential is constant so this results in electric force lines always needing to be perpendicular to equipotential lines in order for the distance to be constant from the charges as well. The direction of the electric field lines is in the direction of the negative charge however, the field is not uniform. Our MATLAB simulation was similar with our experimental results. When talking about errors in the lab, we found errors when we looked at and compared them to the outputs of the MATLAB graphs. The error that we saw was from the u-shaped probe because it was not sturdy at all and was very flimsy so it made it difficult to get the exact point to mark and could have been off compared to where it actually should be. The board is also another reason for error as it was used previously

and developed scratches on it along with the board being uneven which could result in why we had slightly curved center equipotential lines along with other equipotential lines not being symmetric. Despite this, our graphs were similar to the ones from MATLAB which shows how our error was relatively small. The lines that are drawn on the graphs are there to show the parts where voltage is measured and where it is the same at every point. The lines of force are different compared to the voltage lines because force has both magnitude and direction while voltage only has magnitude which is seen from the perpendicular lines to the equipotential lines being the lines of force. The force that would be used on a test charge if it was in the field is displayed through the force lines. 5. Conclusion: After conducting this experiment, it has given us a better understanding of both electric fields and electric potential. It also allowed us to get a better understanding of what electric fields will look like. Even with there being errors we were still able to compare the MATLAB output with our graphs and understand the visualization along with the theory behind it. After concluding this experiment, no further questions are raised however, there could be improvements to the design in order to get better results by reducing error from making sure that the board is new and has little damages/scratches and to have a different tool other than the u-shaped probe that is more steady in order to get more accurate results and reduce error.

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