ece107_set3_nbg

ece107_set3_nbg - ECE 107 Electromagnetism Set 3 Review of...

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1 ECE 107: Electromagnetism Set 3: Review of vector analysis Instructor: Prof. Vitaliy Lomakin Department of Electrical and Computer Engineering University of California, San Diego, CA 92093
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2 Time domain Maxwell s equations: Why do we need vector analysis? Maxwell s equations t ∇× = B E t ∇× = + D H J ρ ∇⋅ = D 0 ∇⋅ = B Basic quantities: 2 ( , ) electric field ( , ) magnetic field ( , ) electric flux density ( , ) magnetic flux density t V m t A m t C m t E r H r D r B r 2 2 3 webers electric current density charge density m A m C m ρ J
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Scalar fields Single value function that depends on position
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Vector fields A vector is given for each position in space Velocity of each atom flow of heat A z A y A x A a A a A z y x ˆ ˆ ˆ ˆ ˆ + + = = = 1 ˆ = a
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Vector fields A vector is given for each position in space A z A y A x A a A a A z y x ˆ ˆ ˆ ˆ ˆ + + = = = ( ) ( ) ( ) B A z B A y B A x B A C z z y y x x + + + + + = + = ˆ ˆ ˆ A B C A A A A z y x 2 2 2 + + =
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Vector fields Position Vector: From origin to point P Distance Vector: Between two points
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