ECE-305-Lecture10

# ECE-305-Lecture10 - Engineering Electro-Magnetics...

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Engineering Electro-Magnetics Engineering Electro-Magnetics ECE-305, Lecture 10 Dennis McCaughey, Ph.D. 4 March, 2010

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03/04/2010 Dennis McCaughey, ECE305, Spring 2010 2 Homework Homework 5.15 5.16 Due March 15
03/04/2010 Dennis McCaughey, ECE305, Spring 2010 3 Current Current An increment of charge, , which moves a distance in a time , produces a component of current density in the limit of v x v x Q S L x t J v ρ = ∆ ∆ = Electric charges in motion constitute current Current is defined as the motion of positive charges even though current in metals is due to the movement of electrons in amps dQ I dt =

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03/04/2010 Dennis McCaughey, ECE305, Spring 2010 4 Current Density Current Density 2 Current Density in amps/meter The increment of current crossing an incremental surface normal to the current density is in the case where the current density is not perpendicular to the sur s I S I J S ∆ = face The total current is s I I d ∆ = • ∆ = J S J S For a volume charge: Assume 1) charge element has its edges parallel to the coordinate axes 2) it only possesses an component of velocity The charge has moved in a time v v v Q v S L x x t Q S x I ρ = ∆ = ∆ ∆ = ∆ ∆ Taking the limit we have where represents the component of is a convection current is a convection current density v v x x s v x v Q x S t t I Sv v x v J v and v I = = ∆ = = = J J
03/04/2010 Dennis McCaughey, ECE305, Spring 2010 5 Continuity of Current Continuity of Current ( 29 ( 29 ( 29 ( 29 ( 29 1) 2) 3) 4) 5) 6) 7) s i s s vol v vol vol v vol vol v v I d dQ I d dt d dv d dv dv dt dv dv t v v t t ρ = = = - = ∇ • ∇• = - ∇• = - ∇• ∆ = - ∇• = - J S J S J S J J J J J Ñ Ñ Ñ 1) Any region bounded by closed surface. The outward flow of positive charge must be balanced by a decrease in positive charge or an increase in negative charge 2) Required by the principle of conservation of charge; I.e. positive or negative charge can neither be created nor destroyed, although they may be simultaneously created destroyed or lost by recombination. Integral for of the continuity equation

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## This note was uploaded on 09/13/2011 for the course ECE 305 taught by Professor Staff during the Spring '08 term at George Mason.

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ECE-305-Lecture10 - Engineering Electro-Magnetics...

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