  We write the spherical curl transformation for Trkalian fields using
differential forms. Then we consider Radon transform of these fields. The Radon
transform of a Trkalian field satisfies a corresponding eigenvalue equation on
a sphere in transform space. The field can be reconstructed using knowledge of
the Radon transform on a canonical hemisphere. We consider relation of the
Radon transformation with Biot-Savart integral operator and discuss its
transform introducing Radon-Biot- Savart operator. The Radon transform of a
Trkalian field is an eigenvector of this operator. We also present an Ampere
law type relation for these fields. We apply these to Lundquist solution. We
present a Chandrasekhar-Kendall type solution of the corresponding equation in
the transform space. Lastly, we focus on the Euclidean topologically massive
Abelian gauge theory. The Radon transform of an anti-self-dual field is related
by antipodal map on this sphere to the transform of the self-dual field
obtained by inverting space coordinates. The Lundquist solution provides an
example of quantization of topological mass in this context.
