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Electromagnetic Wave Equation 
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#1
Sep114, 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. 


#2
Sep114, 08:12 AM

Homework
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Thanks
P: 13,059

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. 


#3
Sep1514, 12:57 AM

P: 107

What is the best text book on PDE's that cover greens function in detail?



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