Answer: The direction of the propagation of the wave in each case are;
A) +z direction
B) +z direction
C) -y direction
D) -x direction
Explanation:
\vec Ein is the Electrical field vector and \vec Bin is the Magnetic field vector, because the field vectors are always perpendicular to each other the propagation of the wave is perpendicular to the two vectors. The direction of the propagation of the wave can be found by \vec Ein X \vec Bin (Cross product of two vectors). This can also be done by using the RIGHT HAND RULE.
Cross product can be found by
i x j = k and j x i = - k
j x k=i and k x j = - i
k x i=j and i x k = - j
where i represents the +x direction, j represents the +y direction and k represents the +z direction
The RIGHT HAND RULE can be used to illustrate the cross product by using the right hand and pointing the index finger in the direction of the first vector and the middle finger along the second vector, the cross product is in the direction of the thumb.
A) \vec Ein the +xdirection,\vec Bin the +ydirection,
Finding the cross product of the two vectors (i x j = k) would give a vector in the +z direction
B) \vec Ein the -y direction,\vec Bin the +x direction
Finding the cross product of the two vectors (- j x i = k) would give a vector in the +z direction
C) \vec Ein the +z direction,\vec Bin the -x direction
Finding the cross product of the two vectors (k x - i = - j) would give a vector in the -y direction
D) \vec Ein the +y direction,\vec Bin the -z direction
Finding the cross product of the two vectors (j x - k = - i) would give a vector in the -x direction
