Duality rotations of Maxwell fields residing in curved space-time are studied in the presence of sources, and it is shown that a general duality rotation transforms the conserved, magnetic-charge-free four-current of a Maxwell field into a new four-current which is neither conserved nor is free of magnetic charges. The necessary and sufficient condition for two Maxwell fields, in the presence of source four-currents which are both conserved and are free of magnetic charges, to go into each other under a duality rotation is obtained. As duality rotations preserve the electromagnetic energy tensor $E_{\mathrm{ab}}$, this leads to conditions under which a given $E_{\mathrm{ab}}$, and hence a given metric solution of the Einstein equations for a continuous system having $E_{\mathrm{ab}}$ as a part of it, may possess a multiple (or in particular, a dual) interpretation in terms of the electromagnetic field. In the case of non-null electromagnetic fields with vanishing Lorentz force, it is shown that a direct computation involving the given Maxwell field yields the required duality rotation provided it exists. A number of examples of duality-connected field pairs, some existing in vacuum and some others inside matter, are discussed to illustrate the theory developed.

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