The term "potential (emf) " has no meaning in non conservative fields. Then why is it included in faraday 's law of induction which deals with induced electric field which is a non conservative field. 

Actually, the term potential has quite confused me. :

1. In the explanation of

$\oint\vec{E}\cdot\mathrm{d}\vec{S} = -\frac{\mathrm{d}\phi}{\mathrm{d}t}$ 

My book (resnick halliday physics part 2) has written that :

> 
> Because this flux is changing with time, an induced emf will appear *around the loop.*
> 
> 
> 

What does the italicised phrase mean? 
In a conservative field we think of potential difference between two points. How is potential developed around the loop considered?