312ps3 - PROBLEM SET 3 ECE 312 Autumn Quarter 2010 Assigned...

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PROBLEM SET 3 ECE 312 Autumn Quarter 2010 Assigned: October 8th Due: October 15th in class Instructor: Joel Johnson Problem 1: For each of the following E fields (i) calculate the corresponding magnetic field from Faraday’s law, and (ii) determine if the electric/magnetic field pair satisfies Maxwell’s equations in regions of free space where J ρ V 0 = = . Note in the equations below, c 1 μ 0 ε 0 --------------- = . (a) E x ˆ 2 t 2 z c ----- + cos = (b) E x ˆ t x c -- sin = (c) E y ˆ 2 z ˆ 5 ------------- t 2 y z + c 5 -------------- + cos = Problem 2 State whether or not the following sets of fields satisfy appropriate boundary conditions for the specified regions. If a surface charge or surface current density is required on the boundary, specify this charge or current density. If a boundary condition is violated, specify this boundary condition. (a) Region 1: ε 1 3 ε 0 = , μ 1 μ 0 = Region 2: PEC. Region 1 exists for y 0 > . E 1 y ˆ z ˆ xy = , H 1 0 = E 2 0 = , H 2 0 = (b) Region 1: ε 1 2 ε 0 = , μ 1 μ 0 = Region 2: ε 2 3 ε 0 = , μ 2 2 μ 0 = . Region 1 exists for z 0 > . E 1 2 zy ˆ 3 z ˆ + = , H 1 3 y ˆ z ˆ = E 2 6 5 -- zy ˆ 2 z ˆ + = , H 2 3 y ˆ z ˆ + = (c) Region 1: ε 1 ε
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