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We have calculated the directed flow v_{1} and charge-dependent directed flow Δv_{1} of pions and protons in Au+Au collisions at sqrt[s_{NN}]=200 GeV by solving the coupled Boltzmann-Maxwell equations self-consistently. Our numerical results show that v_{1} for pions and protons are all negative in the positive midrapidity region and have similar behavior and magnitude. In contrast we find a quite different behavior in Δv_{1} for pions and protons. The difference lies in that Δv_{1} for protons mainly comes from pressure gradients of the medium, while the dominant contribution to Δv_{1} for pions is from electromagnetic fields. Our results indicate that the effect of the electric field will slightly exceed that of the magnetic field and lead to a small negative slope of Δv_{1} for pions.