Question

2. The electric field in a plane wave is described by the equation (k > 0): Ē(x,y,z,1)= E, sin(kz – mt)ị Answer the following questions about the wave. i. What direction is the wave traveling? Explain how you can tell from the equation for the electric field. ii. Write an expression for the magnitude of the magnetic field of the wave. iii. Calculate the average intensity of the wave if Eo = 3000 V/m. The MKS units of intensity are W/m². iv. Atz=1/4 and t=0, in what direction is the magnetic field pointing? V. Below are three equations for a magnetic field. Which is the correct form for this wave? For each, explain why it does or does not describe the correct magnetic field. Please mark all the reasons that a choice cannot be correct. A. B(x,y,z,t) = B sin(kz + @t) B. B(x,y,z,t) = B. cos(ky – ot) c. B(x,y,z,1)= B, sin(kx – motyî D. B(x,y,z,1)= B, sin(kz – (1)(-i)

Answer 1

I) The wave is traveling along  Z direction. It is given by the direction of propagation wave vector K.  

II) Magnitude of the magnetic field will be given by
Bo = " (3 x Ēo)
. Evidently E and B are in phase and mutually perpendicular; their amplitude are related by
Bo =
.

III) average intensity is given by I =
09032

x3 x 108 x 8.854 x 10-12 x (3000)
  
1.2 x 10 W/m

U we have given È (niyitt) = Eosni (kz Wt) j This means ware is transeling along Sin z direction, Electre field at y direction Magnetic field is guenby bo= & 2 x E) & ( 2x Eo (KZ-Wt) }) & Colikz-wt) & xf ] A x 9 = 2 1 B = E K2 - wt) (-2) ý 72 = 7 = Eo sin (kz -WE) (-1) ²x ² = These are cyclic Bosin (KzWt) (2) Now we have Bu = Bo Siri (Kz wt) (?) K= 217 and at 2=7 and at too B = Bosin ( 21. &-0) (-1) - Bosin(17) (-1) Bo (1) FT) = Bo(-1) pointing Bol bointing towards tres x direction

IV) along negative x direction.

V) option D should be correct. Because the direction of magnetic field is given by cross product of propagation vector K and E. To satisfy the cross product (right hand thumb rule) it must be along negative x direction (-i) . Other options are not satisfying the criteria, that's why those options should be correct. (please refer part (II) & (IV)) .

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