| Abstract: | As already demonstrated by R. Wald in 1974, when a spinning black hole (BH) with angular momentum J is immersed in an asymptotically uniform magnetic field of magnitude B, an induced electric field forms in the vicinity of the BH, which in turn forces selective accretion of charges into the BH. Wald argued, by energetic considerations, that the BH will charge up to a universal saturation charge Q=2BJ, often referred to as Wald's charge. However, a recent work by our group has shown that within a simple and elementary accretion model, for which the setup reduces to a scattering problem, a BH charged to Wald's charge accretes charges of both signs in an imbalanced manner – implying that Wald’s charge cannot be regarded as a universal saturation charge. In this work, we calculate analytically (as well as verify numerically) the correct saturation charge within this well-motivated accretion model. We show that despite the fact that Wald's energetic argument proved to be flawed, for strong enough magnetic fields, Wald's charge remains (to leading order) a good approximation for the saturation charge – with a small deviation which we quantify |