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True or False: A time constant electric current density generates both an electric and magnetic field
True or False: An electric current density that is sinusoidal time varying generates both an electric and magnetic field, which in turn are also sinusoidal time varying
True or False: For something to be considered a wave, it only needs to be a sinusoidally time variant field
True or False: The magnetic current density $\overline{J}_m$ is a real physical quantity that contributes to the generation of the electric field along with the magnetic field
True or False: When a wave is time harmonic, the wave equation of said wave becomes dependent on the frequency of the wave
Given a magnetic field as $\overline{H} = \left( 2y\hat{a}_x + 3x\hat{a}_y - 2\hat{a}_z \right)e^{-j2z} $ and an electric current density of $\overline{J}_e = 4\hat{a}_x + 2y\hat{a}_y +z^2\hat{a}_z $ , find the electric field at the point $\left(1,2,-3\right)$ assuming all fields are sinusoidally time variant
Given an electric field as $\overline{E} = \left( 3xz\hat{a}_x + 4yz\hat{a}_y - xy\hat{a}_z \right)e^{-jz} $ and a magnetic current density of $\overline{J}_m = 4x\hat{a}_x + 6y\hat{a}_y -z\hat{a}_z $ , find the electric field at the point $\left(4,-2,0\right)$ assuming all fields are sinusoidally time variant
Given an electric current density of $\overline{J}_e = \left( xyz\hat{a}_x + 2yz\hat{a}_y + 5x^2z^2\hat{a}_z \right)e^{j\omega t}$, a magnetic current density of $\overline{J}_m= \left( 2x\hat{a}_x - 3xy\hat{a}_y - y^2\hat{a}_z \right)e^{j\omega t}$, and relative permeability and permeability of $\mu_r=4$ and $\epsilon_r=5$, find the current sourced wave equation for the magnetic field at the point $\left(2,1,1\right)$
Given an electric current density of $\overline{J}_e = \left( 3z\hat{a}_x - 4x\hat{a}_y + x\hat{a}_z \right)e^{j\omega t}$, a magnetic current density of $\overline{J}_m= \left( xy\hat{a}_x + yz\hat{a}_y - x\hat{a}_z \right)e^{j\omega t}$, and relative permeability and permeability of $\mu_r=2$ and $\epsilon_r=2$, find the current sourced wave equation for the electric field at the point $\left(2,4,8\right)$
Given a field in which there is only an electric current density $\overline{J}_e = \left( 2x^2\hat{a}_x + 2y^2\hat{a}_y - 3x^2z^2\hat{a}_z \right)e^{j\omega t}$, find the current sourced wave equation for the magnetic field at point $\left( 2,2,1 \right)$