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Unformatted text preview: 14 Faraday’s law and induced emf Michael Faraday discovered (in 1831, less than 200 years ago) that a changing current in a wire loop induces current flows in nearby wires — today we describe this phenomenon as electromagnetic induction : current change in the first loop causes the magnetic field produced by the current to change, and magnetic field change, in turn, induces 1 (i.e., produces) electric fields which drive the currents in nearby wires. Definitions of E and B have not changed: recall that • E is force per unit sta tionary charge • B gives an additional force v × B per unit charge in motion with velocity v in the mea surement frame. • While static electric fields produced by static charge distributions are unconditionally curlfree, timevarying electric fields produced by cur rent distributions with timevarying components are found to have, in accordance with Faraday’s observations, nonzero curls specified by ∇ × E = ∂ B ∂t Faraday’s law at all positions r in all reference frames of measurement. Using Stoke’s theorem , the same constraint can also be expressed in integral form as C E · d l = S ∂ B ∂t · d S Faraday’s law for all surfaces S bounded by all closed paths C (with the directions of C and d S related by right hand rule). 1 Relativistic derivation of static B given in Lecture 12 can be extended to show that Coulomb interactions of charges in timevarying motions require a description in terms of timevarying B and E — see, e.g., Am. J. Phys. : Tessman, 34, 1048 (1966); Tessman and Finnel, 35 , 523 (1967); Kobe, 54 , 631 (1986). Thus, the cause of induced E is not really the timevarying B , but rather the timevarying current J producing the variation in B . Still, we find it convenient to attribute the induced E to timevarying B mainly because Ampere’s law provides an explicit link of a timevarying J to B (see Lect’s 12 and 16). 1 • The right hand side of the integral form equation above includes the flux of rate of change of magnetic field B over surface S . If contour C bounding S is stationary in the measurement frame, then the equation can also be expressed as C E · d l = d dt S B · d S , where the right hand side includes the rate of change of magnetic flux Ψ ≡ S B · d S that is independent of S (so long as bounded by C , by Stoke’s theorem)....
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This note was uploaded on 06/20/2011 for the course ECE 329 taught by Professor Kim during the Spring '08 term at University of Illinois, Urbana Champaign.
 Spring '08
 Kim
 Electromagnet

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