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Electromagnetic Wave Equation

by rppearso
Tags: electromagnetic, equation, wave
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rppearso
#1
Sep1-14, 04:54 AM
P: 107
Is it possible to solve these partial differential equations directly, relating to Antenna Theory;

[tex]∇^2 E - μ_0 ε_0 \frac{∂^2E}{∂t^2} = -μ_0 \frac{∂J}{∂t}.[/tex] AND [tex]∇^2 B - μ_0 ε_0 \frac{∂^2B}{∂t^2} = -μ_0 ∇ x J.[/tex]

I don't like the idea of having to make up fields that don't exist in order to make the math work. The x is a cross product not a variable or multiplication.
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Simon Bridge
#2
Sep1-14, 08:12 AM
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Here, let me help with that:[tex]\nabla^2 \vec B - \mu_0 \epsilon_0 \frac{\partial^2\vec B}{\partial t^2} = -\mu_0 \nabla \times \vec J.[/tex]... better? (Hit "quote" to see how I did that.)

There may be some geometries where the equations can be solved directly, I've not heard of any for antennas. Follows that you have to use a Trick. Welcome to realmaths.
rppearso
#3
Sep15-14, 12:57 AM
P: 107
What is the best text book on PDE's that cover greens function in detail?


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