Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. In vector calculus, a vector potential is a vector field whose curl is a given vector field. This is analogous to a scalar potential, which is a scalar field whose negative gradient is a given vector field. An interesting question is then if any solenoidal vector field admits a vec ...Full description
Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. In vector calculus, a vector potential is a vector field whose curl is a given vector field. This is analogous to a scalar potential, which is a scalar field whose negative gradient is a given vector field. An interesting question is then if any solenoidal vector field admits a vector potential. The answer is affirmative, if the vector field satisfies certain conditions. A generalization of this theorem is the Helmholtz decomposition which states that any vector field can be decomposed as a sum of a solenoidal vector field and an irrotational vector field. This nonuniqueness leads to a degree of freedom in the formulation of electrodynamics, or gauge freedom, and requires choosing a gauge.