Electricity and Magnetism

35–236 Electricity and Magnetism

Reflecting on the non-localisable aspect of the induced EMF, and on the fundamental def-

inition of potential difference in terms of the line integral of the local electric field, one

is inspired to recast the LHS of Faraday’s Law in terms of the circulation of the induced

electric field, i.e.,

ε =

I

γ

0

→

E

i

· d~s = Circ



→

E

i



.

This is almost counterintuitive, in that γ

0

is a closed path, and one cannot help but expect

the net potential difference around any closed loop to be zero [`a la Kirchoff’s Second Rule].

These concerns are ameliorated by realising two things:

(1) Kirchoff’s Rules apply to steady state current flows [and stationary ...