If the loop C is a conductor that carries current I in the direction of integration around the loop, and the magnetic flux is due to that current, we have that Φ Φ B = L I , where L is the self inductance of the loop. If in addition, the loop includes a coil that extends from point 1 to 2, such that the magnetic flux is largely localized to that region, it is customary to speak of that region as an inductor, and to consider that its emf is localized to that region. Then, we can consider a different loop C ′ that consists of the coiled conductor from 1 to 2, and an imaginary line down the center of the coil from 2 back to 1. The magnetic flux, and emf, in loop C ′ is essentially the same as that in loop C : E C = E C ′ = − − d Φ Φ C ′ d t = − − L d I d t = ∮ ∮ C E ⋅ ⋅ d ℓ ℓ = ∫ ∫ 1 2 E c o n d u c t o r ⋅ ⋅ d ℓ ℓ − − ∫ ∫ 1 2 E c e n t e r l i n e ⋅ ⋅ d ℓ ℓ .