PlanetPhysics/Lamellar Field

A vector field \,,\, defined in an open set of , is\, lamellar \, if the condition is satisfied in every point \,\, of .

Here, is the curl or rotor of .\, The condition is equivalent with both of the following:

  • The line integrals taken around any closed contractible curve vanish.
  • The vector field has a scalar potential \, \, which has continuous partial derivatives and which is up to a constant term unique in a simply connected domain; the scalar potential means that

The scalar potential has the expression where the point may be chosen freely,\, .\\

Note. \, In physics, is in general replaced with\, .\, If the is interpreted as a force, then the potential is equal to the work made by the force when its point of application is displaced from to infinity.