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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.

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-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?

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  • \$\begingroup\$ Counter-clockwise is positive direction (remember this from trigonometry: how the angles are placed on the unit circle). Also remember the right hand rule. \$\endgroup\$ Oct 29 '20 at 19:12
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The resulting E around the closed loop will be in such a polarity as to produce a current that would, in turn, produce a changing flux that opposes the changing flux that caused the E.

Lenz’s law tells us that “Nature abhors a changing flux”.

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