# Consider a bound atomic electron of charge q in a dielectric medium...

## Question

Show transcribed text

## Transcribed Text

Consider a bound atomic electron of charge q in a dielectric medium with a complex, fre- quency dependent, atomic polarizability a(w). We can write O = a1 + where a1 and a are the real and imaginary parts of O respectively. The dielectric function may be taken to be €(w) = 1 + where N is the density of polarizable atoms. We take = 1 for this medium. Note: for this problem you should not assume any particular functional form for a(w). An oscillating electric field E(t) = Re ] exerts a force on the bound electron cloud. Assume Ew is a real valued vector and s is an arbitrary phase factor. a) [5 pts] The resulting velocity of the electron cloud center of mass can be written as = . Find Vw in terms of Ew and a(w). b) [10 pts] If W is the work done on the electron by the electric field in one period of oscillation T, then find the average work done over one period, i.e. W/T, where T = 2TT/W. This is the energy absorbed by the electron. Express your answer in terms of Ew and a(w). c) [10 pts] Consider a linearly polarized electromagnetic plane wave traveling in the +2 direction. The electric field of this wave can be written as, = = where the complex wavenumber k = K1 + ik2 is related to the complex dielectric function E = E1 + iE2 by k2 = (w2/e2)E(w). Assume the material has a cross-sectional area A in the xy plane. Using your results from (b), find the total energy per unit cross-sectional area, per period of oscillation, that is absorbed by the medium in the half space Z > 0. Express your answer in terms of Ew, E, w and k. d) [10 pts] The magnetic field of this electromagnetic wave can be written as - wt + where k = Ki} + K2 and the phase shift P = tan (k2/k1). Taking the Poynting vector for this wave as S = (c/4m)E X B, show that the total energy per unit cross-sectional area, per period of oscillation, which flows through the plane at Z = 0 is just equal to the energy absorbed by the half-space of the material at Z > 0, as computed in part (c). This is as it must be, since the energy dissipated in the half-space Z > 0 must equal the energy flowing into the half-space through the plane at Z = 0.

## Solution Preview

These solutions may offer step-by-step problem-solving explanations or good writing examples that include modern styles of formatting and construction of bibliographies out of text citations and references. Students may use these solutions for personal skill-building and practice. Unethical use is strictly forbidden.

By purchasing this solution you'll be able to access the following files:
Solution.pdf.

# 50% discount

Hours
Minutes
Seconds
\$52.00 \$26.00
for this solution

or FREE if you
register a new account!

PayPal, G Pay, ApplePay, Amazon Pay, and all major credit cards accepted.

### Find A Tutor

View available Physics - Other Tutors

Get College Homework Help.

Are you sure you don't want to upload any files?

Fast tutor response requires as much info as possible.
{"ft_lang_label":"__label__en","ft_lang_prob":0.8461902,"math_prob":0.97515154,"size":2466,"snap":"2022-40-2023-06","text_gpt3_token_len":670,"char_repetition_ratio":0.101543464,"word_repetition_ratio":0.061269145,"special_character_ratio":0.2485807,"punctuation_ratio":0.08416834,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.99531424,"pos_list":[0,1,2,3,4,5,6,7,8],"im_url_duplicate_count":[null,null,null,null,null,null,null,null,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2022-10-07T13:12:03Z\",\"WARC-Record-ID\":\"<urn:uuid:ec47aa94-1015-44c1-9a78-44382e79a05e>\",\"Content-Length\":\"102114\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:44d22013-5229-4266-96dc-656f7a87446b>\",\"WARC-Concurrent-To\":\"<urn:uuid:6acd4be5-879f-4878-bc57-b52c2510edea>\",\"WARC-IP-Address\":\"52.71.156.158\",\"WARC-Target-URI\":\"https://www.24houranswers.com/college-homework-library/Physics/Physics-Other/63051\",\"WARC-Payload-Digest\":\"sha1:5EGE26DOEQFI46WILZCIQTRXZ6CMG6CT\",\"WARC-Block-Digest\":\"sha1:WCHFWMCFOVDZKVPMCHAA6KXOIO6ER4EN\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2022/CC-MAIN-2022-40/CC-MAIN-2022-40_segments_1664030338073.68_warc_CC-MAIN-20221007112411-20221007142411-00763.warc.gz\"}"}