Abstract: The dual symmetry and transformations in classical electromagnetic theory are reviewed. Then the dual relation between the Aharonov-Casher and He-McKellar-Wilkens topological phases related to the electromagnetic interaction is discussed. Finally, we provide the general Lagrangian for the Aharonov-Casher and He- McKellar-Wilkens topological phases and construct a model independent dual relation between the Aharonov-Casher and He-McKellar-Wilkens topological phases by assuming that the electromagnetic interaction with magnetic monopole violates parity symmetry hut consistent with the relativity.

Key words: Aharonov-Casher phase, He-McKellar-Wilkens phase, dual symmetry