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The interaction between dust grains is an important process in fields as diverse as planetesimal formation or the plasma processing of silicon wafers into computer chips. This interaction depends in large part on the material properties of the grains (for example, whether the grains are conducting, nonconducting, ferrous, or nonferrous). This paper considers the effects that electrostatic and magnetic forces, alone or in combination, can have on the coagulation of dust in various environments. A numerical model is used to simulate the coagulation of charged, charged-magnetic, and magnetic dust aggregates formed from a ferrous material, and the results are compared to each other as well as to those from an uncharged nonmagnetic material. The interactions between extended dust aggregates are also examined, specifically looking at how the arrangement of charge over the aggregate surface or the inclusion of a magnetic material produces dipole-dipole interactions. It will be shown that these dipole-dipole interactions can affect the orientation and structural formation of aggregates as they collide and stick. An analysis of the resulting dust populations will also demonstrate the impact that grain composition and/or charge can have on the structure of the aggregate, as characterized by the resulting fractal dimension.