---
tag: ZSQSPGBN88
kind: concept
name: Method of images
msc: [31B10, 35J08, 78A30]
sources:
  - url: https://en.wikipedia.org/wiki/Method_of_image_charges
same_as:
  wikidata: Q1372220
  wikipedia: Method of image charges
---

## Summary

The method of images builds the [[Green's function|M36SD56MWQ]] of a domain from the potential of a point charge by adding fictitious charges outside the domain.
The image charges are chosen so that the total potential is zero on the boundary.
It gives explicit Green's functions for half-spaces, balls, wedges with special angles and strips.
In physics it solves electrostatic problems with grounded conductors.

## Explanations

### L1 human

A point charge near a grounded flat metal plate behaves as if the plate were replaced by an opposite charge at the mirror point behind it.
On the plate the two potentials cancel, so the plate condition holds automatically.
For the half-space $x_3 > 0$ with a unit charge at $x$, the image is a charge $-1$ at $(x_1, x_2, -x_3)$.
For a sphere, the image sits at the inverse point and has a rescaled strength.