Helmholtz decomposition of surface electric current in electromagnetic scattering problems

In view of the Helmholtz theorem of vector calculus, the surface electric current induced on a conducting body is decomposed into lamellar and solenoidal parts. The solenoidal component is derivable from the normally directed surface curl of the current, and the lamellar component is derivable from the surface divergence (or surface charge) of the current. This representation is an alternative to specifying directly the two scalar components of the surface current. The physical interpretation of the surface curl of the surface current is examined. Examples of scatterers with induced surface currents that are purely lamellar, purely solenoidal, or a combination of both components are cited. A physical feel for the nature of the surface current induced on scatterers is developed, and computational simplifications offered by the Helmholtz decomposition are examined.< >