Question

The magnetic field in a plane monochromatic electromagnetic wave with wavelength A = 445 nm, propagating in a vacuum in the 2-direction is described by B=(Bj sin(kz - wt)(i+1) where 8, = 8.6 X 10ºT, and 1-hat and juhat are the unit vectors in the *x and +y directions, respectively. 1) What is k, the wavenumber of this wave? m Submit 2) What is max, the distance along the positive z-axis to the position where the magnitude of the magnetic field is a maximum at t = 0? nm Submit 3) What is Enax, the amplitude of the electric field oscillations? V/m Submit 4) What is Ey, the y-component of the electric field at (x = 0, y-0, z Zmax) at t = 0? V/m Submit 5) Which of the following equations describes the spatial and time dependence of the electric field oscillations? 12 = fra sin ke – wy}r+1) B={Smsin(ke-me)}. =) = {font cinc - ar}(3-1) Be the cole- an]6 B={Sm.coske–)}– B-flor.cols-cy}23-1) 12 Submit 6) What is tmax, the first time after t = 0, when the magnitude of the electric field at the origin (x = y = z = 0) has its maxiumum value? Submit 7) Compare Ex1 and Exz, the values of the x-component of the electric field at t = 0. Ex is evaluated at (x = 0, y = 0, z = Imax), while Exz is evaluated at (x = 1 nm, y = 1 nm, z = max). Ex1 <EX2

Answer 1

B(B, ain(Kz-wut) (t+S) BIZ8610-6 4 d2445 nm 44SXIO m wawe no.(K) 2 2T 211 Ki 141195175 m zuill be mayimum wshen 2 din (Kz-wt) = Kz-wt 2 T 2 As tzogiven) and 2K 2 I125x 10 2(14119517.5) LL1.25 nm Zこ 4n

Bmax |2 BI Cmaxc 2(8:6X106)3X108) (3) Emay maxC Bmax 2 Emar Emax 3648.61 v/m As electoomegnert field u in z dettion B must be in z dioechon Ey- Ey Ly dinus max 3648.61 Sinys 2580 VIm (SCanect oph'on u Eax win (kz-ot Emax Because disechon dlong x is positive andy negah

tad Maxi mum time atter te o A tmax-t tmax 445x1o 4(3X108 Emax 3.708 X1016 secends AEx Ex2