When a cholesteric liquid crystal is sandwiched between two horizontal glass plates with homeotropic anchoring, chiral patterns named cholesteric fingers of first class, are known to occur. When a DC vertical electric field is applied, the Cholesteric Finger is then observed to move perpendicularly to its long-axis with a velocity V⊥. In this paper, we prove analytically that this velocity may be related with the Lehmann rotation effect, and that it may provide a new way to measure the electromechanical coupling coefficient.