We study the first law of entanglement entropy in holographic CFTs. In particular we study the case in which a vector field is present in the bulk, and attempt to show that this adds a U(1) current and an associated chemical potential to the 1st law on the boundary CFT. We begin by looking at the particular case of a black brane solution in the Poincare patch of AdS₄ and AdS₅, meant to model a local quench in the boundary theory. This solution is obtained by performing a coordinate transformation on the static AdS-RN solution in the global patch and then restricting to the Poincare patch. We then consider the near boundary limit of more general perturbations of pure AdS_d for d ≥ 4.