The origin of galactic and extragalactic magnetic fields is an unsolved problem in modern cosmology. A possible scenario comes from the idea that these fields emerged from a small field, a seed, which was produced in the early universe (phase transitions, inflation, etc.) and it evolves in time. Cosmological perturbation theory offers a natural way to study the evolution of primordial magnetic fields. The dynamics for this field in the cosmological context is described by a cosmic dynamolike equation, through the dynamo term. In this paper we get the perturbed Maxwell's equations and compute the energy-momentum tensor to second order in perturbation theory in terms of gauge-invariant quantities. Two possible scenarios are discussed. First we consider a Friedmann-Lema\^{\i}tre-Robertson-Walker background without magnetic field, and we study the perturbation theory introducing the magnetic field as a perturbation. In the second scenario, we consider a magnetized Friedmann-Lema\^{\i}tre-Robertson-Walker and build up the perturbation theory from this background. We compare the cosmological dynamolike equation in both scenarios.