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# Calculating Potentials

## Prerequisites

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.

## In-class Content

- Series expansion of potential due to a ring of charge (Extension of previous SGA + 20-30 min)
- Lines of Charge (Lecture: 30 min)

## Homework for Symmetries

- (FiniteDisk)
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.

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)

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.

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

- (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.

- (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.