Research Paper > Lab 2 - Electric Potential and Electric fields

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Arpit Patel Nicholas Arredondo Hanh Nguyen Christopher Arriola Lab 2 - Electric Potential and Electric fields 1. Introduction

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In Lab 2: Electric Potential and Electric fields, we try to determine the electric field from the measurements of equipotential surfaces. An equipotential surface is a surface with all points that have the same electric potential. In other words, the potential difference between any two points on an equipotential surface is zero. On a graph, we represent these equipotential lines as green lines on a 2D surface as electric field lines radiate away from the positive point charge (or radiate towards a negative point charge). It is highly important to know that electric field lines are always perpendicular to equipotential lines.

2. The experiment/procedure

In order to find the electric field, we began this lab by setting up different configurations to get the electric potential of each type of surface with an electric current going directly through the wire to the strips. Using the DAQ we collected .csv files with the recorded electric potential

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lines through each configuration. We tested the electric potential across the following metal strip configurations: •

Dipole; we placed the positive and negative probes on the conductor paper and read the potential without any metal strips

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•

Point-plate charge; linear metal strip with positive probe placed on one end and ground

•

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probe placed on conductor paper approximately at half the length of the metal strip

Spherical configuration; 2 semicircle strips held together in contact to make a circle;

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probes placed similarly to point plate charge

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•

Sharp point configuration; sharp v shaped strip, probes placed similarly to point plate

•

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charge

Arbitrary shape configuration; similar to spherical configuration except with one

semicircle and one sharp v shaped strip with the point directed outwards, probes placed

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similarly to point plate charge

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•

Experiment Part 2 (Electric Field)

•

Dipole to Dipole Field: •

The dipole to dipole field was

accurately represented in the experiment and should very marginal error as shown by the vectors that are “off-axis”. This can

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be attributed to placing of the probes as well as noise from the DAQ. •

Arbitrary Shape Field:

• The Arbitrary shape field behaved closely enough to the theoretical field in terms of direction. As seen in the graph, the field shows a distinct left to right passage which is standard for this

experiment. Discrepancies can be seen near the middle of the graph and this can be

attributed to placing of the metal shape on the conductor paper disrupting the flow of current across the paper. Placing of the probes in terms of distance apart also attributed to

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a weaker field on the left most side.

3. The results and discussion

The results of the electric potential of the sphere, arbitrary shape, sharp point, and point plate charge came out similarly: the range goes around 3.5V-5V. However, the dipole electric potential came out relatively smaller: the range goes around 2.5V-3V and it’s much more stable than the other 4 surfaces (the numbers are increasing at a certain rate and not just jumping up and

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down the range like the other 4 surfaces - this is further proven when we provided the graphs for the dipole configuration compared to the arbitrary surface). This is because when we try to measure bigger surfaces like the arbitrary configuration, we can’t get the data of their full surface areas and we can only cut one part of the area out, therefore getting rather chaotic numbers ranging up and down when the sub-area being calculated is too small. For dipole configuration, since it’s literally 2 charges, we can map out a theoretical area without losing any part of the

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actual surface area at all.

The deviation from theoretical predictions in the lab was made when comparing the electrical and equipotential lines. Theoretically these lines should be perpendicular to each other.

However, when the lines from the experiment are examined, only the dipole conveyed the trend of perfectly perpendicular lines. All other configurations that included the metal strips had

varying angles across the lines. This may be due to an existing charge within the plates, the holes that were in the conductor paper, or electric noise around the experiment. Again, it could also be because of the area used to measure, as mentioned above in how chaotic the data points are instead of constantly increasing for the dipole configuration.

4. Conclusion

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Overall, there are still errors in measuring electric potential for certain big surfaces such as the resulting electric field for arbitrary configuration, mainly because the Python program can’t read large surfaces and result in an error when going out of bounds. Whereas for the dipole configuration, since it doesn’t have a specific surface area, the electric potential data are fairly accurate and result in what you would expect from an electric field graph. But through this lab, we learn more about the relationship between electric potential and equipotential lines with electric field, and get a more accurate pictorial representation of the electric field.

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