Question: Show that E xs = Ae j(k0z+Ï) is a solution of the vector Helmholtz equation, Eq. (30), for k 0 = Ïμ 0 0 and

Show that Exs= Aej(k0z+Ï•)is a solution of the vector Helmholtz equation, Eq. (30), for k0= ωˆšÎ¼0ˆˆ0and any Ï• and A.

d²Exs = -k,Es. dz?

dExs = -k,Es. dz?

Step by Step Solution

★★★★★

3.48 Rating (168 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer
Step: 1 Unlock

We take ... View full answer

blur-text-image
Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock
Step: 3 Unlock

Students Have Also Explored These Related Principles Communications Systems Questions!

Q:

Show that I = I 0 e-t/+ is a solution of the differential equation IR + L dl/ dt = 0 where r = L/R and I0 is the current at t = 0.

Q:

Show that if Ï n (x) and Ï m(x) are solutions of the time-independent Schrödinger equation, Ψ (x, t) = is a solution of the time-dependent Schrödinger...

Q:

Show by direct substitution that Equation 14-48 is a solution of Equation 14-47. Equation 14-47 reads d'x 14-47 dx +b=+ mofx = F, cos ot di? dt x = A cos(@t d) 14-48

Q:

(2) Consider a linear regression model y = XB + , where y E R", X E Rnx(+1), and E ~ N(0, 2 In). We assume that the model contains an intercept. Recall the notations y(i) E R- obtained by removing yi...

Q:

(2) Consider a linear regression model y = XB + , where y E R", X E Rnx(+1), and E ~ N(0, 2 In). We assume that the model contains an intercept. Recall the notations y(i) E R- obtained by removing yi...

Q:

OCaml : Sorted lists Consider the functions for ordered lists from the ordered list.ml le in the code-examples direc- tory of the public class repository: let rec place e l = match l with | [ ] ->...

Q:

calculations (ie., no need to explain every little detail on, for example, NPV calculations for Project X, just show that Project X's NPV is X) and incorporated tables. I would expect the memo to be...

Q:

A possible implementation of insertion sort is given by the following Python code: def insertion_sort (xs, key-identity): for i in range(1, len (xs)): e = xs [1] k = key (e) j=i-1 while j> -1 and key...

Q:

Quality illustration and workings only Exercise 2.15 Consider the intercept-only model Y = a + e with a the best linear predictor. Show that a = E[Y]. Exercise 2.16 Let X and Y have the joint density...

Q:

You are the CEO of a large battery company that has a long and famous history in the design, manufacture, and distribution of different types of batteries that are used in a growing variety of...

Q:

In booksite.elsevier.com/9780124171138, we have the malignant breast tumor size in mm of 250 breast cancer patients. In the data base, draw a random sample of the tumor sizes of n = 50 breast cancer...

Q:

Part A Theodore is a sole trader, who runs a primary production business on a property in Central Queensland. He has run this business since 2000. Theodore presented the following information to...

Q:

2 8 Multiple Choice 1 point Your client. Andy, is in need of assistance in preparing his statement of financial position and statement of cash flows. He earns $ 1 5 0 . 0 0 0 annually and pays 1 . 0...

Q:

In ______________ cultures, members tend to do one thing at a time; in ____________ cultures, members tend to do many things at once. (a) monochronic; polychronic (b) universal; particular (c)...

Q:

You decide to use your body as a Carnot heat engine. The operating gas is in a tube with one end in your mouth (where the temperature is 37.0C) and the other end at the surface of your skin, at...

Q:

A person who has skin of surface area and temperature 30.0C is resting in an insulated room where the ambient air temperature is 20.0C. In this state, a person gets rid of excess heat by radiation....

Q:

(a) Sketch the I C - V CE characteristics in the forward-active region for an npn transistor with β F = 100 (measured at low V CE ), V A = 50 V, BV CBO = 120 V, and n = 4. Use Where M is...

Q:

Suppose your expectations regarding the stock price are as follows: Use Equations 5.11 and 5.12 to compute the mean and standard deviation of the HPR on stocks

Q:

A firm offers terms of 1.6/10, net 30. a. What effective annual interest rate does the firm earn when a customer does not take the discount? ( Use 365 days a year. Do not round intermediate...

Q:

XYZ Corporation Income Statements for year ending December 31 (thousands of dollars) 2014 2013 Sales 1,500.0 1,200.0 Operating costs excluding depreciation 1,275.0 1,020.0 Depreciation 36.0 30.0...