  We explore screening effects arising from a relativistic magnetized plasma
with applications to Big Bang nucleosynthesis (BBN). %Specifically, due to
their small magnetic moments, energies of electrons and positrons can be easily
quantized via Landau quantization. The screening potential which depends on the
thermodynamics of charged particles in the plasma is altered by the magnetic
field. We focus on the impact of screening on the electron capture interaction.
Taking into account the correction in BBN arising from a homogeneous primordial
magnetic field (PMF), we constrain the epoch at which the PMF was generated and
its strength during BBN. Considering such screening corrections to the electron
capture rates and using up-to-date observations of primordial elemental
abundances, we also discuss the possibility of solving the problem of
under-estimation of the deuterium abundance. We find for certain values of the
PMF strength predicted D and $^4$He abundances are both consistent with the
observational constraints.
