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EE2011 Lecture 3 - Electrostatics Parrt II

# I r l j ds e ds s s prof joshua le wei li em research

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Unformatted text preview: ctance dl dl V 1 A l l R ;G . I R l J ds E ds S S Prof Joshua Le-Wei Li, EM Research Group Prof 7 EE2011: Engineering Electromagnetics Electromagnetics Conductors • Example 3 Question: The radii of the inner and outer conductors of a coaxial cable of length l are a and b, respectively. The insulation material has a conductivity . Obtain an expression for G’, the conductance per unit length of the insulation layer. Solution: The total current of I, will be flowing through the area of A=2 rl. Therefore, we have the current density J and electric field E as follows: J I I I ˆ ˆ ˆ Jr r r . ; so E 2 rl Aa 2 rl a ˆ Ir I b ˆ dr E dl r Vab ln . a 2 lr 2l b b Therefore, the conductance per unit length is G1 I 2 G' . b l Rl Vab l ln a Prof Joshua Le-Wei Li, EM Research Group Prof 8 EE2011: Engineering Electromagnetics Electromagnetics Conductors • Joule’s Law – Power dissipated in a conducting medium in the presence of an electrostatic field E is considered. The electron and hole charges are qe ve v and qh The electric force acting on qe and qh are Fe vh qe E vh ve v, respectively. E v and Fh qh E E v. The work (energy) expended by the electric field by the electric field is W Fe l e Fh lh le lh W Fe Fh Fe u e Fh u h t t t E J v where the electron shift velocity is u e P velocity is u h ve E ue vh E uh v l e / t , while the hole shift l h / t. Prof Joshua Le-Wei Li, EM Research Group Prof 9 EE2011: Engineering Electromagnetics Electromagnetics Conductors • Joule’s Law - Continued – Power dissipated in a conducting medium is P E Jdv (W) - Joule' s Law V 2 E dv V E x ds E x dl S E x A E xl Prof Joshua Le-Wei Li, EM Research Group Prof IV 10 l I 2 R (W). EE2011: Engineering Electromagnetics Electromagnetics Conductors • Example 4 Prof Joshua Le-Wei Li, EM Research Group Prof 11 EE2011: Engineering Electromagnetics Electromagnetics Conductors • Example 5 Prof Joshua Le-Wei Li, EM Research Group Prof 12 EE2011: Engineering Electromagnetics Electromagnetics Dielectrics • Dielectrics: Concepts – Induced field is called a is polarization field polarization – Polar and nonpolar materials – Polarization property D = 0E+P – P= 0 eE: • Linear if P |E|; • Isotropic if P//E; • Anisotropic if E and D are in different directions; •...
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