PLEASE describe solution clearly in words Thanks Consider an

PLEASE describe solution clearly in words. Thanks!

Consider an EM plane wave with electric field: (l00 V / m) sin [(0.1m-1)x - (3 times 107 rad / s) t] What is the direction of propagation for this wave? What is the wave\'s wavelength? What is the wave\'s frequency f? Write an equation for the magnetic field of the wave. What is the Poynting vector for this EM wave? What is the time-averaged intensity of the wave in W/m2?

Solution

a) now from the equation we can see that the electric field is in the (j) direction & the equation gives how (E) changes with respect to the (x) direction & by comparison with the EM theory we can say that the direction of propagation is the (x) direction & the minus sign tells us that it\'s going in the positive direction

b+c) the electric field general equation is : E = E sin(K.r - t)

where (E) is the amplitude & (K) is the propagation constant , it\'s a vector whose magnitude is (2/) pointing in the direction of propagation & (r) is the wave disturbance at an arbitrary point in space & in our example it\'s the (x) direction ( note that (r) is a vector )

by comparison our equation with the general one we can determine the next :

K = 0.1 m ====> K = 2/ ====> 0.1 = 2/ ====> = 62.832 m

= 3x10^7 rad/s ====> = 2f = 3x10^7 ====> f = 4.77 MHz or you can find (f) by relation (f = c)

d) E = cB ====> E = cB & E = 100 V/m ====> B = 3.33x10^-7 T

    by EM theory both electric & magnetic fields have the same () & the same () & they are perpendicular to each other & the general magnetic field equation is :

   B = B sin(K.r -t) then , by comparison : B = (3.33x10^-7) sin(0.1X - 3x10^(-7)t) k

   where the (k) in the last of the equation is the (kth) direction ( y direction ) of the magnetic field & we choose this direction because the electric field is in the (j) direction & (K : propagation) is in the (i) direction so the (B) field should be perpendicular to both of them .

e) S = c^2 (E x B) (where (S) is in the direction of (K : propagation) & note that (x) here is a cross product & (sin = sin90° = 1) ----> E & B are perpendicular , so :

|S| = c^2 EB = 26.5 W/m^2

f) S(avg) or I = c(B)^2/(2) = 13.23 W/m^2

Good Luck !!!