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In electromagnetism in flat spacetime, the flux of angular momentum through null infinity, as computed through the stress-energy tensor, depends on both radiative and Coulombic degrees of freedom. In the first half of this talk, I will show that this unexpected property holds more generally for electromagnetism in non-dynamical, asymptotically flat spacetimes. Moreover, I will discuss alternative definitions of angular momentum that, in particular, depend only on radiative degrees of freedom. In the second half of this talk, I will discuss asymptotic charges (such as mass and angular momentum) in Einstein-Maxwell theory, where the metric is now dynamical. One could define these charges by using the same expressions as in vacuum general relativity; however, this prescription results in fluxes for angular momentum that depend on Coulombic degrees of freedom, as they did in the non-dynamical case. An alternative definition is to use the prescription of Wald and Zoupas to define these charges, an approach that can be used for any theory with a Lagrangian formulation. Using this definition, the flux of angular momentum depends only on radiative degrees of freedom.