Image System Symmetries

[alec-glisman]

Review email from John and also check the math out myself. The image system may have identical x, y, and z components.

[alec-glisman]

I went through the derivations analytically and discovered that to have a no-flux wall, the image system must have an identical charge reflected about the wall at z = 0.

Real particle

• Charge: q
• Position: (x, y, z)

Image particle

• Charge: q
• Position: (x, y, -z)

This implies that dipoles will similarly have the same (x, y) positions and have their position and dipole direction reflected about the z-axis. This can be seen simply by exploiting the linearity of Laplace's equation and constructing a finite-sized dipole.