{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

# 329fall08hw6 - ECE 329 1 a Prove the identity Homework 6...

This preview shows pages 1–2. Sign up to view the full content.

ECE 329 Homework 6 Due: Tue, Oct 7, 2008, 5PM 1. a) Prove the identity H · ∇ × E - E · ∇ × H = ∇· ( E × H ) for arbitrary vector Felds E and H by expanding both sides of the identity under the assumption that Cartesian components of E and H are di±erentiable. b) Another important identity is ∇×∇× F = ( ∇· F ) -∇ 2 F , where 2 F on right is known as Laplacian of F and it is deFned in Cartesian coordinates via 2 F ( 2 ∂x 2 + 2 ∂y 2 + 2 ∂z 2 )(ˆ xF x yF y zF z ) . ²or the special case of F = x 2 ˆ x + z ˆ y , show that ∇×∇× F and ( ∇ · F ) -∇ 2 F are equal in consistency with the general identity quoted above. 2. Consider an inFnite surface current J s = - ˆ xJ so cos( ωt ) ³owing on z =0 surface, where J so > 0 is the real-valued amplitude of the surface current measured in A/m units. It is found that J s injects Feld energy into propagating electromagnetic waves away from z =0 plane at an average rate of 1 W/m

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### Page1 / 2

329fall08hw6 - ECE 329 1 a Prove the identity Homework 6...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online