# Confusion regarding a few sign conventions in appyling faraday's law to inductive circuits

In the mit ocw lecture by Prof. Lewin on EMI, He quotes a few statements from here to couple of seconds of the lecture.

I am confused why the sign of $$L\frac{dI}{dt}$$ changes, when we go around and evaluate the closed loop integral in the opposite direction of the current.

By faraday's law , we have

$$\oint_{+\partial \Sigma} \vec{E} \cdot d\vec{\ell} = - \frac{d}{dt} \int_{+\Sigma} \vec{B}\cdot d\vec{A}$$

This seemingly suggest that the negative sign would be only affected by the dot product $$\vec{B}\cdot d\vec{A}$$ , and indeed, the direction of the $$d\vec{A}$$(Area vector) is only affected by the sense of path chosen for $$d\vec{\ell}$$ .

Then, what might be the role of current (not the time derivative of current) in deciding the sign of $$L\frac{dI}{dt}$$ ?