Worked Problem Assignment 3#

Due 6 Oct 23

We have developed tools to create general electrostatic situations. And we have worked with some analytical tools to solve for the electric field. Now you will put these together to solve for the electric field in a specific situation.

Grading Rubric

Remember that a worked problem means the scale of a detailed (e.g., parts a-h) homework problem.

Starting your Analysis#

You will need to orient us to your problem as there are many potential electrostatic situations. You will need to develop an analytical tractable situation that can also be explored using the numerical methods we have developed. You will need to do the following:

  1. Write a paragraph or two describing the system you are investigating. Make sure to explain the parameters and variables.

  2. Explain what you are going to do and why. If you can point us to where things are being done, that’s helpful.

  3. You need to clearly set up your analytical problem. This means write down and explain the equations you are constructing.

Investigating the System#

After you set things up, please conduct an investigation using the tools we have developed in class. The order in which it proceeds is up to you, but make sure the flow is logical and clear. We want to understand how your investigations are going to help you be successful with your projects.

Assignment#

  1. Choose an analytical tractable electrostatic problem that you can solve with Gauss’s Law and/or Coulomb’s Law.

  2. Setup and explain the problem to find the electric field at a point in space where you can.

  3. Take limits of your problem to show that you can make sense of the results.

  4. Extend our plotting tools to three dimensions and plot the electric field of your system.

Looking ahead (earn extra credit)#

If you are looking into these systems and finding them interesting here’s two things you can do to earn extra credit that we will discuss later in the course.

  1. Compare your analytical results to your numerical results at a given location. How do they compare? What are the differences? Why do you think there are differences?

  2. Add a charge to your system that is free to move and numerically integrate the motion of the particle (\(\mathbf{F}=q\mathbf{E}\)).

Submitting your work#

You will upload your work to D2L. It should be a single PDF of your work. If you also write code, please submit the associated files as well. If you do all of this in a Jupyter notebook, please export the notebook as a PDF and submit the notebook and PDF file. If you have any questions, please ask. We want you to enjoy working on these problems.