2016 Final Exam Paper (2).pdf

# Ic energy and force n n m jk j k j 1k 1 v v m m i m c

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       ic energy and force: N N m jk j k j 1k 1 v v m m I m c 1 1 1 W L I I = A.J dv H.Bdv 2 2 2 F I dl B, F W , F W         Boundary Conditions at Interface ; ; ; ; Constants for free space: ; Useful Vector identities and properties: VA V A V A     ; 2 A A A        A B B A A A     ; V 0   ; A 0   Some useful formulas of Electromagnetics: Static Electric Field Steady Current Static Magnetic Field Electrodynamics (Quasi-static field) s 2t 1t 0 E E s 2t 1t J 0 H H n n D D 1 2 n n B B 1 2 ) / ( 10 36 1 9 0 m F ) / ( 10 4 7 0 m H V 0; A 0; VA V A A V        1 2 1 2 1 2 ; t t n n J J J J Gauss's Law: Electrostaticenergyand force Laplace'seqn: enclosed enclosed s c b ba a 0 0 e 0 r N e k k Q e V e k 1 v' 2 Q E ds ; D ds Q E dl V , E V D E P, D (1 )E E E 1 1 W Q V D E dv ; F W , F W 2 2 V         Poisson'seqn: 2 ; V 0 for a homogeneous medium s v' t o J u; I J ds l J E; R ; P E J dv' S J ; e t J 0; RC       Tranformer equation / induced voltage Skindepthandacresistance Hysteresisandeddycurrentlosses C rms m c ac n 2 2 h 2 m e 1 m d EMF N , EMF u B .dl dt B E t V 4.44 fNB S 2 1 l , R D P k B f , P k B f       
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