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We obtain the global-in-time and uniform in Knudsen number $\epsilon$ energyestimate for the cutoff and non-cutoff scaled Vlasov-Maxwell-Boltzmann systemfor the soft potential. For the non-cutoff soft potential cases, our analysisrelies heavily on additional dissipative mechanisms with respect to velocity,which are brought about by the strong angular singularity hypothesis, i.e.$\frac12\leq s<1$. In the case of cutoff cases, our proof relies on two newkinds of weight functions and complex construction of energy functions, andhere we ask $\gamma\geq-1$. As a consequence, we justify the incompressibleNavier-Stokes-Fourier-Maxwell equations with Ohm's law limit.

The incompressible Navier-Stokes-Fourier-Maxwell system limits of the  Vlasov-Maxwell-Boltzmann system for soft potentials: the noncutoff cases and  cutoff cases