  We employ an analytic solution of a magnetized Einstein-Maxwell-dilaton
gravity system whose parameters have been determined so that its holographic
dual has the most similarity to a confining QCD-like theory influenced by a
background magnetic field. Analyzing the total potential of a quark-antiquark
pair in an external electric field, we are able to investigate the effect of
the electric field on the different phases of the background which are the
thermal AdS and the black hole phases. This is helpful for better understanding
the confining character and also the phase transitions of the system. We find
out that the field theory dual to the black hole solution is always deconfined.
However, although the thermal AdS phase describes the confining phase in
general, for the quark pairs parallel to $B$ (longitudinal case) and
$B>B_{\mathrm{critical}}$ the response of the system to the electric field
mimics the deconfinement. We moreover consider the effect of the magnetic field
and the chemical potential on the Schwinger effect. We observe that when we are
in the black hole phase with sufficiently small values of $\mu$ or in the
thermal AdS phase, and for both longitudinal and transverse cases, the magnetic
field increase leads to the enhancement of the Schwinger effect, which can be
termed as the inverse magnetic catalysis. This is deduced both from the
decrease of the critical electric fields and from the decreasing the height and
width of the total potential barrier that the quarks are facing with. However,
by increasing $\mu$ to high enough values, the inverse magnetic catalysis turns
into magnetic catalysis, as can also be observed from the diagram of the
Hawking-Page phase transition temperature versus $B$ for the background
geometry itself.
