ikkepotensielle

Ikkepotensielle is a Norwegian term used in mathematics and physics to describe fields or forces that are not derivable from a scalar potential. Literally meaning "non-potential," it denotes vector fields for which no scalar function φ exists such that the field equals the gradient of φ. Such fields are also commonly called non-conservative or rotational.

In vector calculus the absence of a potential is typically signaled by a nonzero curl: in a simply connected domain a vector field F is not potential if curl F ≠ 0. Physically, ikkepotensielle fields produce path-dependent work: the line integral between two points depends on the chosen path. Examples include magnetic fields (which are solenoidal), fluid velocity fields with vorticity, and electric fields induced by time-varying magnetic fields under Faraday’s law. Forces associated with dissipation, such as kinetic friction, are also non-potential.

Mathematically, the Helmholtz decomposition expresses a reasonable vector field as the sum of a gradient (potential) part and a divergence-free rotational part; the presence of the latter marks the ikkepotensielle character. The distinction between potential and non-potential fields has practical consequences in modelling, conservation laws, and the choice of analytical or numerical methods. The term is primarily used in Norwegian-language texts but corresponds to widely used concepts in global vector analysis and physics.