2.2: Activities

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Things You Will Need

Nothing. The data collection is detailed below, and your task is to organize and analyze it.

The Problem

Electrostatics calculations made by two people provide conflicting predictions for the behavior of the electric field strength in a particular arrangement of conductors, and your task is to analyze data from an experiment performed on this conductor arrangement to determine which of these calculations is correct. The conductor arrangement consists of a conducting disk lying in the same plane and sharing its center with a conducting ring that has a larger radius. Only the part of the electric field that exists in the plane of the two conductors is of interest here.

Figure 2.2.1 – The Conductor Arrangement

calculation A: \(E\left(r\right) \propto \frac{1}{r}\)

calculation B: \(E\left(r\right) \propto \frac{1}{r^2}\)

Data Collection

The experimental set-up is the same as in the Background Material, with the exception of the conductors used. The readings on the voltmeter for the conductors are shown in the figure below.

Figure 2.2.2 – Voltmeter Readings for the Conductors

Unlike the potential mapping performed in the Background Material, this experiment maps potentials at specific distances from the center (rather than probing around, looking for specific potentials). Four readings of potential were taken for each distance from the center, to improve our confidence in the results. These four readings are taken along the north, south, east, and west axes (see figure below). Four different distances are represented (giving a total of 16 voltage measurements). A map of the measurements, along with labels indicating the distances from the center of the measurements is given in the figure below.

Figure 2.2.3 – The Voltage Data Map

Data Analysis and Additional Discussion

Your goal is to determine which of two possible functional forms are correct for \(E\left(r\right)\). The way to make this determination is to use the graphical technique we have seen in previous 9-series labs, which is also outlined in one of the text references in the Background Material. But there is a twist in this case. While your goal is to find the proper function for the electric field, the data collected reflects the electric potential (\(V\left(r\right)\)), which is not the same physical quantity. So you will need to translate the functional tests for electric field into functional tests for electric potential – that is, you need to plot \(V\) against the appropriate functions of \(r\) that correspond to the two functions you are testing for \(E\). The text references given in the Background Material should give you the important relationship between \(V\left(r\right)\) and \(E\left(r\right)\) for the particular symmetry involved in this experiment.

Create a table of your data, from which you will create your two plots.
Plot the data for each of the prospective functions you are testing.
Use your two plots to conclude which of the two proposed functions for electric field as a function of radius is the correct one.
Describe the properties of the equipotential surfaces between the conductors that differ by \(1V\) (i.e. \(1V\), \(2V\), \(3V\), and \(4V\)). Namely, are they equally-spaced, as they were in the experiment performed in the Background Material? Why or why not?
Describe the electric field. Which way does it point for this experiment, and where is it stronger, near the center conductor or the outer one?

Lab Report

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