Question

PHYSICS 306 Problem Set: 5 Due Date: 17.5.18 Consider the plane monochromatic plane waves propagating along z-axis, so E and B are given by; $\mathbf{E}(x, y, z, t) = \mathbf{E}(x, y)e^{i(kz - \omega t)}$, $\mathbf{B}(x, y, z, t) = \mathbf{B}(x, y)e^{i(kz - \omega t)}$ Use Maxwell's equations to show that $\mathbf{E}_x$ and $\mathbf{B}_x$ satisfies the following equations. $( \frac{\partial^2}{\partial x^2} + \frac{\partial^2}{\partial y^2} + (\omega/c)^2 - k^2)\mathbf{E}_x = 0$, $( \frac{\partial^2}{\partial x^2} + \frac{\partial^2}{\partial y^2} + (\omega/c)^2 - k^2)\mathbf{B}_x = 0$.

          PHYSICS 306
Problem Set: 5
Due Date: 17.5.18
Consider the plane monochromatic plane waves propagating along z-axis, so E and B are given by;
$\mathbf{E}(x, y, z, t) = \mathbf{E}(x, y)e^{i(kz - \omega t)}$,
$\mathbf{B}(x, y, z, t) = \mathbf{B}(x, y)e^{i(kz - \omega t)}$
Use Maxwell's equations to show that $\mathbf{E}_x$ and $\mathbf{B}_x$ satisfies the following equations.
$(
\frac{\partial^2}{\partial x^2} + \frac{\partial^2}{\partial y^2} + (\omega/c)^2 - k^2)\mathbf{E}_x = 0$,
$(
\frac{\partial^2}{\partial x^2} + \frac{\partial^2}{\partial y^2} + (\omega/c)^2 - k^2)\mathbf{B}_x = 0$.

PHYSICS 306
Problem Set: 5
Due Date: 17.5.18
Consider the plane monochromatic plane waves propagating along z-axis, so E and B are given by;
𝐄(x, y, z, t) = 𝐄(x, y)e^i(kz - ω t),
𝐁(x, y, z, t) = 𝐁(x, y)e^i(kz - ω t)
Use Maxwell's equations to show that 𝐄x and 𝐁x satisfies the following equations.
(
(∂^2)/(∂ x^2) + (∂^2)/(∂ y^2) + (ω/c)^2 - k^2)𝐄x = 0,
(
(∂^2)/(∂ x^2) + (∂^2)/(∂ y^2) + (ω/c)^2 - k^2)𝐁x = 0.

Added by John E.

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