  The representation of magnetic field as a sum of a toroidal field and a
poloidal field has not rarely been used in astrophysics, particularly in
relation to stellar and planetary magnetism. In this representation, each
toroidal field line lies entirely in a surface, which is named a toroidal field
surface. The poloidal field is represented by the curl of another toroidal
field and it threads a stack of toroidal field surfaces. If the toroidal field
surfaces are either spheres or planes, the poloidal-toroidal (PT)
representation is known to have a special property that the curl of a poloidal
field is again a toroidal field . We name a PT representation with this
property a standard PT representation while one without the property is called
a generalized PT representation. In this paper, we have addressed the question
whether there are other toroidal field surfaces allowing a standard PT
representation than spheres and planes. We have proved that in a three
dimensional Euclidean space, there can be no standard toroidal field surfaces
other than spheres and planes, which render the curl of a poloidal field to be
a toroidal field.
