EE325_quiz_8_sol_Yilmaz

EE325_quiz_8_sol_Yilmaz - NAME Solution 1 Let μ = 3 ×...

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NAME: _____________ Solution I EE325-Fall 2009 Quiz 8 1) Let 5 3 10 H/m μ = × , 10 1.2 10 F/m ε = × , and 0 σ = everywhere. If 10 ˆ 2cos(10 ) A/m z t x β = H a , find the following. Hint: Point form of Maxwell’s equations in a source-free region are: 0, / t ∇ ⋅ = ∇× = −∂ D E B , 0, ∇ ⋅ = B / t ∇× = ∂ H D . a) B (1 point) b) D (4 points) c) E (2 points) d) β (3 points) See HW 9 for solution. EE325-Fall 2009 Quiz 8 1) Consider a metallic conductor with 12 0 8.85 10 F/m ε ε = = × , 7 0 4 10 H/m μ μ π = = , 7 10 S/m σ = that is carrying a current at 60 Hz with current density 6 2 ˆ 10 sin(120 120 ) A/m x t z π = J a . Hint 1: Point form of Maxwell’s equations are: , / v t ρ ∇ ⋅ = ∇× = −∂ D E B , 0, ∇ ⋅ = B / t ∇× = + ∂ H J D . Hint 2: σ = J E in the time varying case. a) Find the electric field strength in the conductor (1 point) 1 ˆ 10 sin(120 120 ) V/m x t z π σ = = J E a b) Find the magnetic flux density in the conductor (3 points) 1 1 1 / ( , , ) ˆ / 120 10 cos(120 120 ) ˆ 120 10 cos(120 120 ) ( , , ) ˆ 10 sin(120 120 ) ( , , ) y x y y t dt x y z E z t z t z dt x y z t z x y z π π π
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