prelim1Solf07 - ECE 303: Electromagnetic Fields and Waves...

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
ECE 303: Electromagnetic Fields and Waves Fall 2007 Solutions for Prelim 1 Reminder: Date: Tuesday 9/25 Problem 1: A current loop above a perfect conductor. a. The image current is a loop of radius a , located at z = - d , and of value - I ( t ) (i.e., opposite direction). b. The z component of the magnetic field due to the original loop is H z ( partial ) = I ( t ) 4 π ± 2 πa a 2 + ( L - d ) 2 sin α = I ( t ) 2 ˆ a 2 [ a 2 + ( L - d ) 2 ] 3 / 2 ! Then the total field is the superposition of the fields produced by each current loop: H z = a 2 I ( t ) 2 ˆ 1 [ a 2 + ( L - d ) 2 ] 3 / 2 - 1 [ a 2 + ( L + d ) 2 ] 3 / 2 ! c. By symmetry, the x component of the field is zero. Problem 2: Finding the electric field with a volume charge and dielectric material. a. The boundary condition at x = d is ε 0 E x ( x = d + ) = ε 1 E x ( x = d - ) where E x ( x = d + ) = E 0 . So, E x ( x = d - ) = ε 0 ε 1 E 0 . The differential form of Gauss’ Law in one dimension is ∂x ( ε 1 E x ( x )) = ρ ( x ) for 0
Background image of page 1
This is the end of the preview. Sign up to access the rest of the document.
Ask a homework question - tutors are online