LAB 2-2

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Jan 9, 2024

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Lab 2: Mapping the electrostatic potential and electric field Group members: Goals: The goal of this lab is to explore the potentials, equipotential curves, and electric fields produced by various two dimensional electrostatic charge distributions. This can be done since we know that the electric force is conservative and therefore can be associated with the electric potential V. With this we can practice visualizing electric fields and practice graphing and analyzing nonlinear relations. Procedure: For part 1 of the lab we have to locate the conductive paper with the point source and ring shield electrode configuration, and then pin the corners of the paper to the cork board. We then take a cable with a banana plug on one end, and a ring terminal on the other, and plug the banana end into the positive power supply, then pin the ring terminal end of the cable to the central point electrode using a metal pushpin. Then we connect the negative of the power supply to the shield ring. Turn on the power supply at 5 V, and check the electrodes for conductivity. Then make a potential graph For part 2 of the lab we will replace the point source electrode with the electric dipole configuration and connect the leads to the 5V source. Then place the black reference voltage probe halfway between the two electrodes, and the red probe on the paper. Then map out multiple equipotential curves nearer and farther from the point charges. For part 3 of the lab we have to set up the configuration necessary, and then map out multiple equipotential curves near the point charges and near the walls of the box. For part 4, we have to connect the parallel plate electrodes to a power supply, and then measure the potential every 0.5cm from the midpoint of the negative electrode to the midpoint of the positive electrode. Error and precautions: Whilst we did not have any errors in our own experiment, there could be potential errors in reading the voltmeter, or if the conductivity of the electrodes is reduced. Precautions included setting up the equipment correctly, ensuring that the banana end and the shield ring were attached to the correct equipment, and that the voltmeter probes were placed well on the conductive paper, to give us an accurate reading.

Results: Point charge mapping: Point charge data: distance (cm) voltage (v) 1/d 1 2.2 1 1.5 1.473 0.666667 2 1.063 0.5 2.5 0.685 0.4 3 0.422 0.333333 3.5 0.175 0.285714 4 0.008 0.25

Point charge graphs:

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Electric Dipole equipotential and mapping: Like charges equipotential and mapping: Parallel plates data: distance (cm) voltage (v) 0 0 0.5 0.485 1 0.858 1.5 1.353 2 1.755 2.5 2.2 3 2.66 3.5 3.05 4 3.47 4.5 3.86 5 4.39 5.5 4.68 6 5.02

Questions: 1. Does your graph show a linear dependence between potential and distance? Theoretically, what should be the relationship between potential and distance as you move away from a point charge? a. For the graph of potential vs distance we can see a logarithmic dependance. Theoretically the relationship should be 1/r 2 which aligns with our results 2. What are the shapes of equipotentials in the region around a point source? Do your results agree with the equipotentials shown in Figure 1?

a. The shape of the equipotential for the point charge represents a circle around the point charge. This matches figure 1 exactly. 3. Does the potential vary much from one point to another outside of the shield ring? What does this imply about the electric field outside the shield ring? Refer to equation 1 for help with your answer. a. Outside of the shield ring we can see the potential energy drop off drastically. Looking at equation 1 we can see that the electric field strength follows an inverse relationship to the distance which aligns with what we saw. 4. Note all but one of the equipotential lines for a dipole are curved, where is the uniquely straight equipotential line for a dipole? a. The uniquely straight equipotential line for a dipole is at the center of the dipole, specifically the middle axis that runs from the positive to the negative end of the dipole. 5. Relative to this halfway point, where on the conducting paper is the potential highest (most positive)? Where is it the lowest (most negative)? a. Relative to the halfway point, the potential is the highest when it is the closest to the positive charge, and the lowest when it is closest to the negative charge. 6. Referring to your graph, describe how the potential changes with distance from the electrode. How does this contrast to the potential vs distance for a point source you found in part 1? a. The potential increases linearly with distance from 0V to 5V, which was the input. This is the opposite to the potential vs distance graph, which decreased as the distance increased. The two relations are inversely related. 7. Theoretically, what is the physical meaning of the slope of your graph? Data in your graph to a line and use your slope to find and report the value of the electric field between the two plates and report the value in units of V/m. a. The slope of the graph represents the rate of change of the electric field potential per unit distance between the two plates. Using our data our calculated value was 0.0085 V/m. Discussion: From this lab we were able to observe visualizations of electric fields for point charges, opposing dipoles, matching dipoles and parallel plates. With our observations and data from our experiments we were able to graph and analyze nonlinear relationships of our data.

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