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Recently, the rapidity-odd directed flow ( v 1 ) of produced hadrons ( K − , ϕ , p ¯ , Λ ¯ , Ξ ¯ + , Ω − , and Ω ¯ + ) has been studied. Several combinations of these produced hadrons, with very small mass differences but differences in the net electric charge ( Δ q ) and net strangeness ( Δ S ) on the two sides, have been considered. A difference in v 1 between the two sides of these combinations ( Δ v 1 ) has been proposed as a consequence of the electromagnetic field produced in relativistic heavy-ion collisions, especially if Δ v 1 increases with Δ q . Our study is performed to understand the effect of the coalescence sum rule (CSR) on Δ v 1 . We point out that the CSR leads to Δ v 1 = c q Δ q + c S Δ S , where the coefficients c q and c S reflect the Δ v 1 of produced quarks. Equivalently, one can write Δ v 1 = c q Δ q + c B Δ B , involving the difference in the net baryon number Δ B , where the CSR gives c B = − 3 c S . We then propose two methods to extract the coefficients for the Δ q and Δ S dependences of Δ v 1 . [ABSTRACT FROM AUTHOR]