Calculating Potentials

Students should be able to:

• Find the electric potential from a system of discrete point sources.
• Write the difference vector between two vectors (and its magnitude).
• (Optional) Write charge densities in terms of delta functions.
• Compute line integrals.
• Find power series approximations.

1. (FiniteDisk)

   1. 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. Find the electrostatic potential everywhere along the axis of symmetry due to a finite disk of charge with uniform (surface) charge density $\sigma$. Start with your answer to part (a)

   3. 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.

2. (InfiniteDisk)

   Find the electrostatic potential due to an infinite disk, using your results from the finite disk problem.

3. (PotentialConeGEM227)

   A conical surface (an empty ice-cream cone) carries a uniform charge density $\sigma$. The height of the cone is $a$, as is the radius of the top. Find the potential at point $P$ (in the center of the opening of the cone), letting the potential at infinity be zero.

4. (WritingII)

   Using the handout “Guiding Questions for Science Writing” as a guide, write up your solution for finding the electrostatic potential everywhere in space due to a uniform ring of charge. Be sure to include a series expansion along one of the axes of interest.