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The properties of nuclear matter under extreme conditions of high temperature, density, and isospin asymmetry have attracted wide attention in recent years. At present, heavy ion reactions in combination with corresponding model simulations are one of the most important ways to investigate this subject. It is known that a strong magnetic field can be created in heavy ion collisions. However, its effect on the motion of charged particles is usually neglected in previous transport model simulations. In this work, within the ultrarelativistic quantum molecular dynamics (UrQMD) model, the temporal evolution and spatial distribution of the internal magnetic field are calculated. The magnetic field strength is found to reach about $eB\ensuremath{\approx}470\phantom{\rule{4pt}{0ex}}{\mathrm{MeV}}^{2}$ ($B\ensuremath{\approx}8\ifmmode\times\else\texttimes\fi{}{10}^{16}$ G) for Au $+$ Au collisions at ${E}_{\text{lab}}=1\phantom{\rule{0.16em}{0ex}}\mathrm{GeV}/\mathrm{nucleon}$ with impact parameter of 7 fm. The magnetic field in Cu $+$ Au collisions exhibits somewhat different spatial distribution from that in Au $+$ Au collisions. The magnetic field is found to affect the directed flow of pions at forward and backward rapidities to some extent, dependent of the impact parameter and beam energy while the effect on the elliptic flow is small. In addition, the effects of the magnetic field on the ${\ensuremath{\pi}}^{\ensuremath{-}}/{\ensuremath{\pi}}^{+}$ ratio over the whole rapidity range and the elliptic flow difference ${v}_{2}^{n}\text{\ensuremath{-}}{v}_{2}^{p}$ between neutrons and protons at forward and backward rapidities are on the same order as those from the nuclear symmetry energy. The ${v}_{2}^{n}\text{\ensuremath{-}}{v}_{2}^{p}$ difference in the midrapidity region is not strongly affected by the magnetic field, and the total ${\ensuremath{\pi}}^{\ensuremath{-}}/{\ensuremath{\pi}}^{+}$ yield ratio is immune to it. It is advisable to include the magnetic field effects in future studies using pion flow, pion yield ratio, and nucleon elliptic flow difference to probe the symmetry energy at super saturation densities.