Zangwill's book of Electrodynamics studies the orders of magnitud of the Maxwell 's Equations. When analysing the last one which includes displacement current, only the time variation of the zero-curl-component of the electric field is used.

$ j = \frac{\partial E_{c}}{\partial t} $

Where $E_{c}$ means the coulomb field or zero-curl component. Mi question is why the Faraday component is not used. When I integrate over a closed surface the last Maxwell Equation, it is clear the Faraday component vanishes using divergence theorem since it's divergence is zero. However, the analysis is made locally and there I don't see reason for it to not be considered.



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