Quiz - Electromagnetic Plane Wave Propagation

True or False: Faraday's Law can be simplified down to $\bigtriangledown \times \overline{E} = -j\omega \overline{B}$ when the fields are time harmonic.

True or False: A wave equation relates the double derivative with respect to space to the double derivative with respect to time.

True or False: The time harmonic portion of an equation, $e^{j\omega t}$, must always be included in notation.

Given the following solution to the wave equation with respect to the x direction, which case for $ k_x^2 $ results in a propagating solution?

$ \frac{d^2 X(x)}{dx^2} + k_x^2 X(x) = 0 $

Which of the following terms results in a positive propagation in it's respective direction, assuming that the respective wave numbers are positive.

Which of the following boundary conditions is incorrect when considering a plane wave intersecting at a planar boundary, as shown below?

Given that $\mu = 6\mu_0 $, $\epsilon = 2\epsilon_0$, and $f=2.5GHz$, what is the wave number of a wave traveling with these characteristics?

Given a material that has the properties $\mu = 1.5\mu_0 $ and $\epsilon = 7.25\epsilon_0$, what is the phase velocity of a wave traveling in this material?

Find the electric field in region 2 of the following setup, assuming that $ \overline{E}_1=(2\hat{a}_x + 12\hat{a}_y - 6\hat{a}_z)e^{-jz} $, $ \rho_s=y^2z^2 $ $\epsilon_1 = 3.5$, and $\epsilon_2 = 2.25$.

Find the magnetic field in region 2 of the following setup. Assume $ \overline{E}_1 = ( x^2y^3 \hat{a}_x - 3y\hat{a}_y + 5xyz\hat{a}_z)e^{-jz} $, $ \overline{J}_s = 2x^2\hat{a}_x - 4xy \hat{a}_y $, $ \mu_1 = 5 $, and $ \mu_2 = 4 $

Find the surface current of the following setup. Assume $ \overline{E}_1 = ( 12y \hat{a}_x +3xy\hat{a}_y +x^2y\hat{a}_x=z )e^{-jz} $, $ \overline{E}_2 = ( xy \hat{a}_x +x^2y^2\hat{a}_y +x^3y^3\hat{a}_x=z )e^{-jz} $, $ \mu_1 = 1 $, and $ \mu_2 = 2 $