Jason Wang

The top two pictures are my original hypothesis of the electric field of the two setups. In the circular setup, the electric field points radially outwards and decreases in magnitude as it goes further away from the center. In the parallel plates setup, the electric field was constant. The bottom two pictures are my revised hypothesis with equipotential lines and data points for the change in voltage. The circular setup diagram confirms that my original hypothesis was correct and that the electric fields were greatest where the equipotential lines were densest. The parallel plates diagram has incorrectly drawn equipotential lines. I thought they were densest near the positive side but was actually constant. The constant equipotential lines corresponds with the constant electric field.

Jason Wang

Data for Circle Data for Parallel Plates

Jason Wang

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Voltage Inside a Ring

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Voltage Inside a Ring (ln scale)

The data for the circle configuration is most linear when it is graphed as V vs. ln(distance). This is consistent with a 2d setup. The integration of the electric field with respect to r for a 2d setup results with V inversely proportional to ln(r).

Jason Wang

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Voltage between Parallel Plates

The data for the parallel plate setup is linear without any manipulation. The derivative of this graph would be a constant horizontal line, consistent with parallel paltes.

5. In this lab, we measured the change in electric potential of two setups and drew equipotential lies for each. In our circular setup, we found that the equipotential lines were denser in the center, and in our capacitor setup we found the lines to be uniformly distributed. Electric potential is equal to the integral of the electric field with respect to R. We found that where the equipotential lines were densest and the change in voltage was greatest, the electric field was also greatest. Additionally, we found that the voltage decreased proportionally to ln(r). In the case of the capacitor, we found the electric field to be constant. These results verify Gauss’ law, which states that the electric field in a 2d setup is inversely proportional to R.

Jason Wang