PHY2061 R. D. Field Department of Physics chp38_2.doc University of Florida ClosedSurface SVolume ChargeDensity ρJCurl of the Electric Field Consider a fixed coil with varying current I. If Cis a closed curve, stationary in the O-frame, and if Sis a surface spanning C, and ),,,(tzyxBris the magnetic field measured in the O-frame at time t, then ∫⋅=CrdErrεand ∫⋅=ΦSBAdBrr. Faraday&s Law of induction tells us that dtdBΦ−=and Stoke&s Theorem says ∫∫⋅×∇=⋅SCAdErdErrrrr)(. Thus,∫∫∫∫⋅∂∂−=⋅−=⋅×∇=⋅SSSCAdtBAdBdtdAdErdErrrrrrrrr)(which implies that tBE∂∂−=×∇rrrCharge Conservation:
This is the end of the preview. Sign up
access the rest of the document.
This note was uploaded on 05/31/2011 for the course PHY 2061 taught by Professor Fry during the Spring '08 term at University of Florida.