### Diagnostics: Calculating or Approximating the Electostatic Potential
d.ems.ca

Fundamentals: After properly studying this module, you should be able to:

- state the uniqueness theorem for solutions to Poisson's equation
- explain the method of images
- explain the method of separation of variables
- write down the monopole and dipole terms of a general charge distribution \(\rho ({\bf r})\)

Applications: As a strict minimum, you should be able to:

- for all points \({\bf r}\), write down the electrostatic potential generated by a point source charge \(q\) at \({\bf r}_s\) with an infinite grounded conducting plane at \(z = 0\)
- write down the generic solution to Laplace's equation for an infinitely long rectangular pipe with the four edges at arbitrary potentials (no need to solve it: just write down the generic solution, and the boundary conditions which would in principle fix all the parameters)
- reproduce the solution for the potential generated by a sphere with surface charge density \(\sigma_0 (\theta)\) (in the example in the notes, which you can here use for inspiration)
- sketch the electric field of a dipole

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Author: Jean-Sébastien Caux

Created: 2022-03-24 Thu 08:42