Electrostatic Forces (PHYS142 - 2022)

Introduction

In this experiment you will measure the electrostatic force between plates of a parallel plate capacitor and compare your results with predictions derived from Coulomb's Law which can be written as,

$F=\frac{1}{4 \pi \epsilon_{o}} \frac{q_{1}q_{2}}{r^{2}}$.

The constant $\epsilon_{o}$ is called the permittivity of free space.

This is a challenging measurement to make because the forces involved are small and fall off quickly as the plate separation increases. Making accurate measurements with small enough uncertainties to meaningfully test the model will require not only careful measurements, but also a detailed study of instrumental effects which may possibly bias the data. This is an extremely important point to consider when doing experimental physics. You can make the most careful measurement possible, with the smallest uncertainties and still end up with data that point to a completely incorrect conclusion if you have not properly accounted for biases in your data which are inherent in your experimental technique. Note that virtually all experiments have to deal with these sorts of biases which are more commonly referred to as systematic uncertainties. So a major learning goal of this experiment is learning how to setup an experiment, collect initial data, evaluate the data, think about ways to improve the measurement, make additional measurements to assess and quantify the impact of possible systematic effects and then put all that information together to come up with deeper and more meaningful conclusions.

The experiment will be done over two consecutive lab periods.

  • For the first week you will focus on determining what Coulomb's Law predicts about how the force between the capacitor plates should depend on factors such as plate separation and voltage, making measurements to test those predictions and then evaluating how well the data compare to the model.
  • The second part of the experiment on the second week will focus on making additional measurements to assess and quantify the effect of instrumental biases which may be present in your data from the previous week, determining how to account for these biases in your measurement and then seeing how this changes your final conclusion.

First Week

Predicting the Relationship Between F, D and V

Begin by using your knowledge of the physics of electrostatics and capacitors to come up with a relationship which describes how the force between the plates of a parallel plate capacitor varies as a function of both the voltage difference between the plates and the distance between the plates.

Your TA will guide you through this process and it should take no more than 30 minutes. If you have not yet gotten to some of the relevant concepts in lecture do not be concerned, the TA will help to fill in these gaps. The purpose of this exercise is to gain experience applying the physics concepts which you see in lecture to a real physical system that you will then test.

Collecting Data to Test the Prediction

The Apparatus

The experimental apparatus is pictured above and consists of the following.

  • A scale capable of measuring up to 200g, on which the bottom plate of the capacitor sits.
  • An assembly which holds the top plate of the capacitor in a fixed position.
  • A base on which the scale sits. The height of the base relative to the fixed position of the top capacitor plate can be precisely controlled using three micrometer screws.
  • A variable 1500V power supply to apply a voltage difference between the top and bottom plates of the capacitor.
  • A set of 5 20g masses.
  • A single 200g mass.
  • A precision ball bearing attached to the end of a wand.
  • A ruler.

Taken together these components can be used to calibrate the scale, accurately set and adjust the spacing between the capacitor plates while maintaining a fixed high voltage and measuring the force between the plates.

High voltage power supply

We will charge the plates with a power supply, adjustable to about 1500 volts. You will use the output labeled 20 MΩ. The high voltage cable should be plugged into the small box on the left side of the apparatus. This box contains a 100 MΩ resistor, which serves to limit the current to a safe value to avoid shock hazard.

SHOCK HAZARD


Even though the power supply is current limited for safety, you can still receive a shock from the potential difference. The power supply should be OFF any time cables are being connected or disconnected. Avoid touching the capacitor plates while the voltage is on.

Second Week

Independent of whether or not your data are in agreement with the model or disagreement, as an experimentalist it is important that you are properly interpreting the data. For example your data may be in agreement with the model based on the uncertainties which you estimated. But how do you know if that agreement is correct and not an artifact of some unknown bias? Alternatively if your data are in disagreement with the model based on your estimated uncertainties, there is still a possibility that something about how you did the experiment introduced a bias in the data which is not related to the uncertainties that you recorded.

The issue of biases in experiments is not about whether or not you made a “mistake”, or is your equipment “good enough”. It is also not the result of the fact that you are using teaching lab apparatus instead of “good” apparatus like you would see in a research lab. Anytime you measure something your measurement device is interacting with that which you are measuring, and so the possibility of instrumental bias always exists.

For this experiment the second lab period is devoted to identifying, quantifying and accounting for one of the sources of instrumental bias that exists in the apparatus. Your TA will lead you through a discussion of possible sources of biases that might impact your measurement and how you might go about investigating the impact of the bias. Then you will conduct what is essentially another experiment, collecting and analyzing data in order to determine how to better interpret your results from last week.

Experimental Procedure

Group reports


For each lab, you will receive a template file that you will flesh-out as you go along through the lab.

Select one group member to be the record-keeper. This person will be the primary person who fills out the group report, but _all_lab partners are expected to contribute ideas, data and arguments to the document, and everyone should agree with the final report before submission. The role of the record-keeper will change every week so that all students share in the responsibility.

Use the link below to get a copy of the file for this lab, and add your group members' names to the document. As soon as your new document opens, be sure to share it with all members of the group by selecting “Share” in the upper right corner and adding their UChicago email addresses.

Note that you will have to log into your UChicago google account using your CNETID.

Lab Report Template

Using Jupyter notebook


After the discussion, you will continue taking data. In order to visualize this data, we again provide a Google Colaboratory notebook to make calculations and to plot as you go.

Assignment submission and grading

Make sure to submit your lab notebook by the end of the period. Download a copy of your notebook in PDF format and upload it to the appropriate spot on Canvas. Only one member of the group needs to submit to Canvas, but make sure everyone's name is on the document!

For the first week of this lab there will be no individual summary and conclusions, you will be graded on participation and your group notebook. Your individual summary and conclusions are due after the second part of the lab.