Solenoidal Vector Field
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High Quality Content by WIKIPEDIA articles! In vector calculus a solenoidal vector field is a vector field v with divergence zero: nabla cdot mathbf{v} = 0., The fundamental theorem of vector calculus states that any vector field can be expressed as the sum of an irrotational and a solenoidal field. The condition of zero divergence is satisfied whenever a vector field v has only a vector potential component, because the definition of the vector potential A as: mathbf{v} = nabla times mathbf{A} automatically results in the identity (as can be shown, for example, using Cartesian coordinates):nab...
High Quality Content by WIKIPEDIA articles! In vector calculus a solenoidal vector field is a vector field v with divergence zero: nabla cdot mathbf{v} = 0., The fundamental theorem of vector calculus states that any vector field can be expressed as the sum of an irrotational and a solenoidal field. The condition of zero divergence is satisfied whenever a vector field v has only a vector potential component, because the definition of the vector potential A as: mathbf{v} = nabla times mathbf{A} automatically results in the identity (as can be shown, for example, using Cartesian coordinates):nabla cdot mathbf{v} = nabla cdot (nabla times mathbf{A}) = 0. The converse also holds: for any solenoidal v there exists a vector potential A such that mathbf{v} = nabla times mathbf{A}.
