As the model magnetic cloud moves past the earth, an observe (e.g. a satellite) sees a magnetic field varying in time. In this example, the northward component (Bz>0) arrives at the earth first (Chen, 1996). The continued expansion in the minor radial direction is taken into account. Although no ambient magnetic field is included outside the cloud edges (the vertical dashed lines), the solar wind typically has fluctuating field of roughly 5nT in magnitude. A nonzero by outside the flux rope will cause theta (panel c) to decrease. The By and Bz components and theta are shown. The above theoretical model closely resembles the observed magnetic cloud. The By component, which is in the east-west direction, peaks where Bz= 0. The sign difference in By cloud wind speed V and density are also shown. The major gaps in the data are indicated by vertical dashed lines.