  We investigate the space-time dependence of electromagnetic fields produced
by charged participants in an expanding fluid. To address this problem, we need
to solve the Maxwell's equations coupled to the hydrodynamics conservation
equation, specifically the relativistic magnetohydrodynamics (RMHD) equations,
since the charged participants move with the flow. To gain analytical insight,
we approximate the problem by solving the equations in a fixed background
Bjorken flow, onto which we solve Maxwell's equations. The dynamical
electromagnetic fields interact with the fluid's kinematic quantities such as
the shear tensor and the expansion scalar, leading to additional non-trivial
coupling. We use mode decomposition of Green's function to solve the resulting
non-linear coupled wave equations. We then use this function to calculate the
electromagnetic field for two test cases: a point source and a transverse
charge distribution. The results show that the resulting magnetic field
vanishes at very early times, grows, and eventually falls at later times.
