The potential difference between two points is given ans the negative of integral of E(vector) <dot product> dl(vector) from initial to final points.
Therefore, integral integral of E(vector) <dot product> dl(vector) from initial to final point should give the negative of potential difference between them.
In Faraday's law, closed loop integral of E(vector) <dot product> dl(vector) is given as ε- induced. Why is it not the negative of ε-induced. Should ε-induced not be treated like potential difference?