Perform the following steps to verify by substitution that equations c and D are
ID: 1535314 • Letter: P
Question
Perform the following steps to verify by substitution that equations c and D are solutions to Equations A and B, respectively. a2E a2E E Emax cos(kx at? Equation A Equation C a2B B B,max cos(kx Eoko wt) dt 2 Equation B Equation D (a) Calculate the first partial derivatives listed below (Use the following as necessary: k, x t and either Emax or B, DE dx aB dE aB (b) Calculate the second partial derivatives listed below. (Use the following as necessary: k, a, x, t, and either Emax or Bmax.) d2E ax2Explanation / Answer
(a)E = Emax*cos(kx -wt)
dE/dx = -k*Emax*sin(kx-wt)
B = Bmax*cos(kx -wt)
dB/dx = -k*Bmax*sin(kx-wt)
E = Emax*cos(kx -wt)
dE/dt = w*Emax*sin(kx-wt)
B = Bmax*cos(kx -wt)
dB/dt = w*Bmax*sin(kx-wt)
(b) d^2E/dx^2 = -k^2*Emax*cos(kx -wt)
d^2B/dx^2 = -k^2*Bmax*cos(kx -wt)
d^2E/dt^2 = -w^2*Emax*cos(kx -wt)
d^2B/dt^2 = -w^2*Bmax*cos(kx -wt)
(c) (d^2E/dx^2)/(d^2E/dt^2) = k^2/w^2
(d^2B/dx^2)/(d^2B/dt^2) = k^2/w^2
(d) (d^2E/dx^2) = (k^2/w^2)(d^2E/dt^2)
(d^2E/dx^2) = (eo*uo)(d^2E/dt^2)
eouo = k^2/w^2 = (1/flamda)^2
eouo = 1/c^2