In low-frequency circuit theory Kirchhoff’s current law assumes that the algebraic sum of conduction currents at a junction is strictly zero. At very high frequencies or in rapidly changing electromagnetic fields this assumption can fail.
(i) State what additional form of current must be considered to restore the continuity of charge at such frequencies.
(ii) Using the concept identified in part (i), explain qualitatively why the algebraic sum of only the conduction currents can be non-zero for a very small Gaussian surface enclosing part of a capacitor plate during charge–discharge at high frequency.
(iii) Show that when this additional current is included, the extended form of Kirchhoff’s current law is once again consistent with the principle of charge conservation.