  We study the static responses of cold quark matter in the intermediate
baryonic density region (characterized by a chemical potential $\mu$) in the
presence of a strong magnetic field. We consider in particular, the so-called
Magnetic Dual Chiral Density Wave (MDCDW) phase, which is materialized by an
inhomogeneous condensate formed by a particle-hole pair. It is shown, that the
MDCDW phase is more stable in the weak-coupling regime than the one considered
in the magnetic catalysis of chiral symmetry braking phenomenon (MC$\chi$SB)
and even than the chiral symmetric phase that was expected to be realized at
sufficiently high baryonic chemical potential. The different components of the
photon polarization operator of the MDCDW phase in the one-loop approximation
are calculated. We found that in the MDCDW phase there is no Debye screening
neither Meissner effect in the lowest-Landau-level approximation. The obtained
Debye length depends on the amplitude $m$ and modulation $b$ of the
inhomogeneous condensate and it is only different from zero if the relation $|
\mu -b| > m$ holds. But, we found that in the region of interest this
inequality is not satisfied. Thus, no Debye screening takes place under those
conditions. On the other hand, since the particle-hole condensate is
electrically neutral, the U(1) electromagnetic group is not broken by the
ground state and consequently there is no Meissner effect. These results can be
of interest for the astrophysics of neutron stars.
