An electromagnetic wave is traveling in a vacuum. At a particular instant for this wave, $\mathbf{E} = [(-52.0)\mathbf{i} + (65.0)\mathbf{j} + (26.0)\mathbf{k}] \, \text{N/C}$, and $\mathbf{B} = [(0.290)\mathbf{i} + (0.200)\mathbf{j} + (0.080)\mathbf{k}] \, \mu \text{T}$.
(a) Calculate the following quantities. (Give your answers, in $\mu \text{T} \cdot \text{N/C}$, to at least three decimal places.)
$E_x B_x = -15.08$
$E_y B_y = 13.00$
$E_z B_z = 2.080$
$E_x B_x + E_y B_y + E_z B_z = 1.776e-15$
Are the two fields mutually perpendicular? How do you know?
Yes, because their dot product is equal to zero.
(b) Determine the component representation of the Poynting vector (in W/m²) for these fields.
$\mathbf{S} = 6.74\mathbf{i}, 9.31\mathbf{j}, -23.38\mathbf{k}$
Apply the definition of the Poynting vector and cross product. W/m²
