vector potential

Let  U=U(x,y,z)  be a vector fieldMathworldPlanetmath in 3 with continuousMathworldPlanetmathPlanetmath partial derivativesMathworldPlanetmath.  Then the following three conditions are equivalentMathworldPlanetmathPlanetmathPlanetmathPlanetmathPlanetmath (

  • The surface integrals of U over all contractible closed surfaces ( S vanish:

  • The divergenceMathworldPlanetmath of U vanishes everywhere in the field (

  • There exists the vector potentialMathworldPlanetmathA=A(x,y,z)  of U:



  • 1 K. Väisälä: Vektorianalyysi.  Werner Söderström Osakeyhtiö, Helsinki (1961).
Title vector potential
Canonical name VectorPotential
Date of creation 2013-03-22 15:42:54
Last modified on 2013-03-22 15:42:54
Owner pahio (2872)
Last modified by pahio (2872)
Numerical id 8
Author pahio (2872)
Entry type Definition
Classification msc 26B12
Related topic IntegrationWithRespectToSurfaceArea
Related topic LaminarField
Related topic KalleVaisala