2018/05/13 by Bob Eisenberg, Eisenberg, Bob, Nathan Gold +5 · 1 citation
Computer Science · Engineering · #Analog and Mixed-Signal Circuit Design #Classical Physics (physics.class-ph) #FOS: Physical sciences #Low-power high-performance VLSI design #Parallel Computing and Optimization Techniques
paper · pdf · doi:10.48550/arxiv.1805.04814
openalex publication_date 2018/05/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Our digital technology depends on mathematics to compute current flow and design its devices. Mathematics describes current flow by an idealization, Kirchhoff's current law. All the electrons that flow into a node flow out. This idealization describes real circuits only when stray capacitances are included in the circuit design. Motivated by Maxwell's equations, we propose that current in Kirchhoff's law be defined as ε 0 \frac∂ \boldsymbolE∂ t + \widetilde\boldsymbolJ, the sum of (1) displacement current (2) the flux of charge associated with mass. The flux of charge associated with mass \widetilde\boldsymbolJ includes, for example, the polarization of dielectrics as well as the movement of electrons. Kirchhoff's law becomes exact and universal when current is defined this way. This current is the source of the magnetic field; it is the source of \boldsymbolcurl\boldsymbol \boldsymbolB in Maxwell's equations. Kirchoff's laws and Maxwell's equations can use the same definition of current.