Solutions to the Yang-Mills field equations in the presence of extended external sources are reviewed. Point sources have qualitatively different solutions than do extended sources. A model of a nonrelativistic particle in an external potential interacting self-consistently with the Yang-Mills field is used to see whether the particle's wave function acts as an extended source. This model is discussed in detail and a gauge, analogous to the London gauge, is used to set up an initial-value problem for its equations of motion. For small gauge coupling $g$ we find no evidence of solutions with lower energy than a simple Abelian solution. Such a lower-energy solution may, however, exist for large coupling.

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