An induced electric field is conservative! The reason is best seen using one of Maxwell's equations of electromagnetism.
Faraday's law describes how a changing magnetic field can create ("induce") an electric field. This aspect of electromagnetic induction is the operating principle behind many electric generators: A bar magnet is rotated to create a changing magnetic field, which in turn generates an electric field in a nearby wire.
From Maxwell's equations of electromagnetism, the Maxwell–Faraday equation, which is a slightly different version of (Faraday's law of induction) takes the vector form: -
∇ x E = -∂B
……...... __
……..…. ∂t
Or in the integral form the equation becomes: -
?E.dl = -∂? B, S
… s ….. __
……….. ∂t
The first term on the left hand side is the line integral of the electric field along the boundary '∂S' of a surface 'S' (∂S is always a closed curve). This integral evaluates in units of joules per coulomb (energy). The right hand term of the equation is the rate of change with time of the magnetic flux ‘?’ within that closed surface.
The flux is calculated from the integral:-
Φ = ∫∫B. dS
……. S
Where, ‘B ‘is the magnetic field and ‘S’ is the surface area and ‘dS’ is an infinitesimal vector, whose magnitude is the area of a differential element of S, and whose direction is the surface normal.
The unit of measurement of the magnetic field is the Weber or joules per ampere.
Thus, the equation is implicitly conservative of energy.
may be this might help ...but mind u this is copy paste stuff......i myself havent read it nicely ...
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