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A higher-order, locally corrected Nyström discretization of an augmented electric field integral equation (EFIE) is developed and demonstrated for low-frequency applications. The augmented system is obtained by combining the EFIE with the current continuity equation. Due to the discontinuous nature of the higher-order Nyström discretization, it is necessary to introduce line charge degrees of freedom on all mesh edges. It is observed that the resulting linear system is stable as the frequency decreases, and it also provides high-order convergence for a canonical geometry.