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Unformatted text preview: EEL 3472 EEL 3472 Time  Varying Time  Varying Fields Fields EEL 3472 EEL 3472 2 TimeVarying Fields TimeVarying Fields TimeVarying Fields Stationary charges electrostatic fields Steady currents magnetostatic fields Timevarying currents electromagnetic fields Only in a nontimevarying case can electric and magnetic fields be considered as independent of each other. In a timevarying (dynamic ) case the two fields are interdependent. A changing magnetic field induces an electric field, and vice versa. EEL 3472 EEL 3472 3 TimeVarying Fields TimeVarying Fields The Continuity Equation Electric charges may not be created or destroyed (the principle of conservation of charge). Consider an arbitrary volume V bounded by surface S . A net charge Q exists within this region. If a net current I flows across the surface out of this region, the charge in the volume must decrease at a rate that equals the current: Divergence theorem This equation must hold regardless of the choice of V , therefore the integrands must be equal: For steady currents that is, steady electric currents are divergences or solenoidal.  = = = S V V dv dt d dt dQ dS J I  = V V V dv t dv J t J V  = = J Kirchhoffs current law follows from this ) / ( 3 m A the equation of continuity Partial derivative because may be a function of both time and space V This equation must hold regardless of the choice of V , therefore the integrands must be equal: EEL 3472 EEL 3472 4 TimeVarying Fields TimeVarying Fields Displacement Current For magnetostatic field, we recall that Taking the divergence of this equation we have However the continuity equation requires that Thus we must modify the magnetostatic curl equation to agree with the continuity equation. Let us add a term to the former so that it becomes where is the conduction current density , and is to be determined and defined. J H = ( 29 J H = =  = t J V d J J H + = J E J E = d J EEL 3472 EEL 3472 5 TimeVarying Fields TimeVarying Fields Displacement Current continued ( 29 d J J H + = = J J d  = ( 29 t D D t t J J V d = = =  = t D J d = H = J + D t xH ds = S J + D t S ds H dl = I + D t S ds L H Taking the divergence we have In order for this equation to agree with the continuity equation,...
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This note was uploaded on 09/26/2011 for the course EEL 3211 taught by Professor Staff during the Spring '08 term at University of Florida.
 Spring '08
 Staff
 Electromagnet

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