# Orders of magnitude of the last Maxwell Equation

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.

Thanks!