An Asymptotic-Preserving DC Limit of Maxwell’s Equations

The steady (DC) limit of Maxwell’s equations is often treated by directly setting time derivatives to zero, but this operation can be mathematically singular and can erase information needed to describe how electromagnetic energy is delivered to dissipative loads in DC circuits. By analyzing the DC limit in the Laplace domain, we show that the correct limiting procedure retains additional terms that restore the missing coupling between electric and magnetic fields and enforce a nonzero power flow into conductors through boundary/interface constraints. This work attempts to clarify the apparent information loss of the usual DC reduction and clarifies the role of field residues in steady power transfer.