  We compute the magnetic field-induced modifications to the boson
self-coupling and the boson-fermion coupling, in the static limit, using an
effective model of QCD, the linear sigma model with quarks. The former is
computed for arbitrary field strengths as well as using the strong field
approximation. The latter is obtained in the strong field limit. The arbitrary
field result for the boson self-coupling depends on the ultraviolet
renormalization scale and this dependence cannot be removed by a simple vacuum
subtraction. Using the strong field result as a guide, we find the appropriate
choice for this scale and discuss the physical implications. The boson-fermion
coupling depends on the Schwinger's phase and we show how this phase can be
treated consistently in such a way that the magnetic field induced vertex
modification is both gauge invariant and can be written with an explicit factor
corresponding to energy-momentum conservation for the external particles. Both
couplings show a modest decrease with the field strength.
