Herein an approach is presented to determine the expansion and distortion of the cross section of magnetic clouds (MCs) in their evolution in the interplanetary medium. This approach, based on the improvement of our previous elliptical cross-section model for the magnetic topology of MCs, gives analytical expressions for $vec B$ and $vec j$ which incorporate the expansion of the cross section of clouds. Our starting point is the assumption of a spatially uniform jη, the normal component of the plasma current density to the cross section of the cloud. As it is described in the text, this expansion provides a time dependency of the three components of the plasma current density. The main physical consequences of this behavior are discussed. Fittings to eight selected MCs of years 2000 and 2001 with different magnetic field profiles are presented.