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Perform the following steps to verify by substitution that equations C and D are solutions to Equations A and B, respectively. E = Emax cos(kx – wt) Equation A Equation C a2B a2B B = Bmax cos(kx – wt) Equation B Equation D (a) Calculate the first partial derivatives listed below. (Use the following as necessary: k, w, x, t, and either Emax or Bmax:) JE -kE тахL [sin (kx – ot)] ax aB -kB max Sin ( kx – wt)] ax ME sin ( kx – ot тах or)] at дв = wB at max[sin (kx – ot)] (b) Calculate the second partial derivatives listed below. (Use the following as necessary: k, w, x, t, and either Emax or Bmax:) a²E cos(kx- ot) əx2 тах cos (kx – ot) тах a?E - -o²E.cos(kx – ot) at? тах a2B .cos(kx – ot) тах (c) Given k2 / w² = (1 / f 1)², calculate the ratios of the second partial derivatives below. (Use the following as necessary: c.) ax2 1 2 a2B a2B (d) Express &oo: (Use the following as necessary: c.) 1

Perform the following steps to verify by substitution that equations C and D are solutions to Equations A and B, respectively. E = Emax cos(kx – wt) Equation A Equation C a2B a2B B = Bmax cos(kx – wt) Equation B Equation D (a) Calculate the first partial derivatives listed below. (Use the following as necessary: k, w, x, t, and either Emax or Bmax:) JE -kE тахL [sin (kx – ot)] ax aB -kB max Sin ( kx – wt)] ax ME sin ( kx – ot тах or)] at дв = wB at max[sin (kx – ot)] (b) Calculate the second partial derivatives listed below. (Use the following as necessary: k, w, x, t, and either Emax or Bmax:) a²E cos(kx- ot) əx2 тах cos (kx – ot) тах a?E - -o²E.cos(kx – ot) at? тах a2B .cos(kx – ot) тах (c) Given k2 / w² = (1 / f 1)², calculate the ratios of the second partial derivatives below. (Use the following as necessary: c.) ax2 1 2 a2B a2B (d) Express &oo: (Use the following as necessary: c.) 1

College Physics
College Physics
11th Edition
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter1: Units, Trigonometry. And Vectors
Section: Chapter Questions
Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...
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part C. 

Perform the following steps to verify by substitution that equations C and D are solutions to Equations A and B, respectively. a²E = Eolo at? E = Emax cos(kx – wt) Equation A Equation C a?B = Eolo at? B = Bmax cos(kx – wt) ax? Equation B Equation D (a) Calculate the first partial derivatives listed below. (Use the following as necessary: k, w, x, t, and either Emax or Bmax:) -kE тахL sin (kx – ot)] ax дв -kB тах — sin (kx – ot)] ax sin ( kx – ot)] at тахL дв @B тах L sin ( kx – ot) at (b) Calculate the second partial derivatives listed below. (Use the following as necessary: k, w, x, t, and either E or Bmax:) max -KE тах cos (kx- ot) ax? a²B -k*B „cos(kx – ot) əx? тах -o²E at? cos(kx – wt) тах a²B -o?B. at? cos(kx – ot) тах (c) Given k2 / w? = (1 / f 1)2, calculate the ratios of the second partial derivatives below. (Use the following as necessary: c.) ax2 at2 a2B a2B at2 (d) Express ɛolo: (Use the following as necessary: c.) Eolo = II
Transcribed Image Text:Perform the following steps to verify by substitution that equations C and D are solutions to Equations A and B, respectively. a²E = Eolo at? E = Emax cos(kx – wt) Equation A Equation C a?B = Eolo at? B = Bmax cos(kx – wt) ax? Equation B Equation D (a) Calculate the first partial derivatives listed below. (Use the following as necessary: k, w, x, t, and either Emax or Bmax:) -kE тахL sin (kx – ot)] ax дв -kB тах — sin (kx – ot)] ax sin ( kx – ot)] at тахL дв @B тах L sin ( kx – ot) at (b) Calculate the second partial derivatives listed below. (Use the following as necessary: k, w, x, t, and either E or Bmax:) max -KE тах cos (kx- ot) ax? a²B -k*B „cos(kx – ot) əx? тах -o²E at? cos(kx – wt) тах a²B -o?B. at? cos(kx – ot) тах (c) Given k2 / w? = (1 / f 1)2, calculate the ratios of the second partial derivatives below. (Use the following as necessary: c.) ax2 at2 a2B a2B at2 (d) Express ɛolo: (Use the following as necessary: c.) Eolo = II
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