Electromagnetic Fields & Waves: Assignment 6 for EE 30348 at Notre Dame, Fall 2008, Assignments of Electrical and Electronics Engineering

Download Electromagnetic Fields & Waves: Assignment 6 for EE 30348 at Notre Dame, Fall 2008 and more Assignments Electrical and Electronics Engineering in PDF only on Docsity! Fundamentals of Electromagnetic Fields and Waves: I Fall 2008, EE 30348, Electrical Engineering, University of Notre Dame Assignment 6 Due date: Friday, Oct 31. Please attach this sheet on top of your solutions. Sketch figures wherever necessary. 1) Electromagnetic Waves (Review question): Here is a question from the 2007 EMag 1st Midterm exam (slightly modified)- The electric field vector of an electromagnetic plane wave propagating in free space is given by E(r, t) = E0 cos(ωt − β0z)ax a) Identify the wavelength, frequency, polarization, and the direction of propagation of the plane wave. b) Write down the expression for the corresponding magnetic field B(r, t). c) Refer to Figure 1. A square conductive loop of side L and total resistance R0 is now placed in the path of the electromagnetic wave as shown. Explain qualitatively why the electromagnetic wave will cause a current to flow in the loop. L x y z Figure 1: A square loop interacts with an electromagnetic wave. d) Find the magnitude of the induced current flowing in the loop. (You may or may not need the following relations: ∫ sin(az)dz = − cos(az) a +C, ∫ cos(az)dz = sin(az) a +C, sin(a) − sin(b) = 2 cos(a+b2 ) sin( a−b 2 ), 1