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Conservation of Current in Five Slides November 13 2017

Conservation of Current is Universal and Exact at all Times and in All Conditions, including inside atoms. This can be shown in three slides, and explained in five slides.

Bob_Eisenberg
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Conservation of Current in Five Slides November 13 2017

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  1. Conservation of Current is Universal and Exact in five slides Bob Eisenberg November 13, 2013 Department of Applied Mathematics Illinois Institute of Technology Chicago and Department of Physiology and Biophysics Rush University, Chicago

  2. Maxwell’s Magnetism ?? ?,? ?? Τ ???? ? ?,? ?0 = ? ?,? + ?0 Current Current is Conserved PERFECTLY ??? ???? ≡ 0 is an identity ?? ?,? ?? ??? ? ?,? + ?0 = ? Current 2

  3. Current has Current has very very Different Different Physics in Different Systems Different Systems Physics in Ag AgCl Ag AgCl     * i E t i D t D = permittivity   E but Continuity Continuity of Current is of Current is Exact ??????? ?= ??????? ?= ??????? ?… Exact no matter what carries the current, at all times and all locations!

  4. Conservation of Current is Exact and Universal ?? ?,? ?? ??? ? ?,? + ?0 = ? Current even though Physics of Charge Flow Varies Profoundly

  5. ?? ?,? ?? = ? ??? ? ?,? + ?0 Current Device 1 Device 2 Displacement Current is Different in Each Device because ? ?,? is Different in every Device so the TOTAL Current is exactly equal at every time in every location and every device Total Current = Displacement Current + Device Current 5

  6. Electric Field takes on the Electric Field takes on the Value that Conserves Current Value that Conserves Current ? ?,? = −1 ?0න? ?,? ?? Specifically, E changes the displacement current ε0 So total current ? ?,? + ε0 Τ ?? ?? ?? ?? is always conserved Τ Details and PROOF including quantum mechanics at https://arxiv.org/abs/1609.09175 Page 6

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