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lam58
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Q) A harmonic time-dependent electromagnetic plane wave, of angular frequency ω, propagates along the positive z-direction in a source-free medium with σ = 0, ε = 1 and µ = 3. The magnetic field vector for this wave is: H = Hy uy. Use Maxwell’s equations to determine the corresponding electric field vector.Ans) I've pretty much forgotten all this stuff from 1st year, so I'm not sure if my answer is correct.
[tex] \bigtriangledown \times H = \varepsilon_0 \frac{\partial E}{\partial t}[/tex], [tex]H = (0, Hy, 0)[/tex]
[tex] \bigtriangledown \times H = \begin{vmatrix} \hat{u}x & \hat{u}y & \hat{u}z \\ \frac{\partial}{\partial x} & \frac{\partial}{\partial y} & \frac{\partial}{\partial z} \\ 0 & Hy & 0 \end{vmatrix}[/tex]
[tex]= \hat{u}x (\frac{-\partial Hy}{\partial z}) - \hat{u}y(0) + \hat{u}z (\frac{\partial Hy}{\partial z}) = (\frac{-\partial Hy}{\partial z}, 0, 0)[/tex]
and
[tex]\varepsilon_0 \frac{\partial E}{\partial t} = (\varepsilon_0 \frac{\partial E}{\partial t}, 0, 0)[/tex]
[tex] \Rightarrow \varepsilon_0 \frac{\partial E}{\partial t} = \frac{-\partial Hy}{\partial z} [/tex]
At this point I'm somewhat lost as how to find E vector. I know that J = σ E and σ = 0, but how do I get from what I got above to the E vector?
[tex] \bigtriangledown \times H = \varepsilon_0 \frac{\partial E}{\partial t}[/tex], [tex]H = (0, Hy, 0)[/tex]
[tex] \bigtriangledown \times H = \begin{vmatrix} \hat{u}x & \hat{u}y & \hat{u}z \\ \frac{\partial}{\partial x} & \frac{\partial}{\partial y} & \frac{\partial}{\partial z} \\ 0 & Hy & 0 \end{vmatrix}[/tex]
[tex]= \hat{u}x (\frac{-\partial Hy}{\partial z}) - \hat{u}y(0) + \hat{u}z (\frac{\partial Hy}{\partial z}) = (\frac{-\partial Hy}{\partial z}, 0, 0)[/tex]
and
[tex]\varepsilon_0 \frac{\partial E}{\partial t} = (\varepsilon_0 \frac{\partial E}{\partial t}, 0, 0)[/tex]
[tex] \Rightarrow \varepsilon_0 \frac{\partial E}{\partial t} = \frac{-\partial Hy}{\partial z} [/tex]
At this point I'm somewhat lost as how to find E vector. I know that J = σ E and σ = 0, but how do I get from what I got above to the E vector?