  We study a five-dimensional perfect fluid coupled with Kaluza-Klein (KK)
gravity. By dimensional reduction, a modified form of Maxwell's equation is
obtained, which is relevant to the equation of state of the source. Since the
relativistic magnetohydrodynamics (MHD) and the 3-dimensional formulation are
widely used to study space matter, we derive the modified Maxwell's equations
and relativistic MHD in 3+1 form. We then take an ideal Fermi gas as an example
to study the modified effect, which can be visible under high density or high
energy condition, while the traditional Maxwell's equation can be regarded as a
result in the low density and low temperature limit. We also indicate the
possibility to test the state-relevant effect of KK theory in a telluric
laboratory.
