Static Fields: Winter-2025
HW 06 : Due 1/24 Fri

  1. Confidence Rating S0 5171S After solving each problem on the assignment, indicate your answers to the following questions for each problem. Answer for the problem as a whole, even if the problem has multiple parts.
    1. Question Confidence How confident are you that you are interpreting the problem the way the instructor intends?

      For the rest of the questions, assume you have interpreted the problem correctly
    2. Problem Confidence How confident are you that you could independently come up with a correct solution process to a similar problem on a future problem set?
    3. Answer Confidence How confident are you that your final answer to this question is correct (not solution process)?
    4. Makes Sense To what degree do you understand how your answer fits (or does not fit) the physical or mathematical situation of the problem?
  2. Charge on a Spiral S0 5171S (8pts) A charged spiral in the \(x,y\)-plane has 6 turns from the origin out to a maximum radius \(R\) , with \(\phi\) increasing proportionally to the distance from the center of the spiral. Charge is distributed on the spiral so that the charge density increases linearly as the radial distance from the center increases. At the center of the spiral the linear charge density is \(0~\frac{\textrm{C}}{\textrm{m}}\). At the end of the spiral, the linear charge density is \(13~\frac{\textrm{C}}{\textrm{m}}\). What is the total charge on the spiral?
  3. Potential from a Finite Disk S0 5171S

    In this problem, in all cases, you are expected to evaluate any integrals in your answers.

    1. (2pts) Starting with the integral expression for the electrostatic potential due to a ring of charge, find the value of the potential everywhere along the axis of symmetry.
    2. (4pts) Find the electrostatic potential everywhere along the axis of symmetry due to a finite disk of charge with uniform (surface) charge density \(\sigma\).
    3. (2pts) Find two nonzero terms in a series expansion of your answer to part (b) for the value of the potential very far away from the disk. [Your final answer should have 2 non-zero terms]