I have a question about direction of vectoral line integral in formula of electric potential and electric field.

• In electrostatic I assumed $$\B\$$ is positive potential and $$\A\$$ is negative potential so the boundary of the integral is negative to positive and also there is a minus sign outside the integral, and also $$\d\ell\$$ direction is always positive. This approach was always true in my electromagnetic 1 class. For example if electric field is negative in the y-direction it means that the upper side is more positive and the lower side is more negative through the y-axis.

-But In electromagnetic 2 according to Faraday's law, time varying magnetic fields create emf. But this time the line integral is closed loop and I am very confused, what should I choose? Which direction is positive and negative and where is the minus sign of the integral? For example if path is a circular loop between 0 to 2$$\\pi\$$ how can I decide the positive and negative direction 0 to 2$$\\pi\$$ or 2$$\\pi\$$ to 0 and where is the minus sign?

• Counter-clockwise is positive direction (remember this from trigonometry: how the angles are placed on the unit circle). Also remember the right hand rule. Oct 29 '20 at 19:12