  We construct a variety of conserved currents for test electromagnetic fields
on a Kerr background. Our procedure, which involves the symplectic product for
electromagnetism and symmetry operators, generates the conserved currents given
by Andersson, B\"ackdahl, and Blue (2015), as well as a new conserved current.
These currents reduce to the sum of (positive powers of) the Carter constants
of photons in the geometric optics limit, and generalize the current for scalar
fields discovered by Carter (1977) involving the Killing tensor. We furthermore
show that the fluxes of our new current through null infinity and the horizon
are finite.
