  We investigate how the presence of RR magnetic $F_{p+2}$ fluxes affects the
energy of classical Dp branes, for specific string theory supersymmetric
backgrounds which are solutions to the leading order in $\alpha'$ including
back-reaction effects. The Dp brane dynamics is found to be similar to the well
known dynamics of particles and strings moving in magnetic fields. We find a
class of BPS solutions which generalize the BPS fundamental strings or BPS
branes with momentum and winding to the case of non-zero magnetic fields.
Remarkably, the interaction with the magnetic fields does not spoil the
supersymmetry of the solution, which turns out to be invariant under four
supersymmetry transformations. We find that magnetic fields can significantly
reduce the energy of some BPS strings and Dp branes, in particular, some
macroscopic Dp branes become light for sufficiently large magnetic fields.
