- #1

Enialis

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I need to solve this general problem. Let's consider the following vector field in cylindrical coordinates:

[tex]\vec{A}=-J'_m(kr)\cos(\phi)\hat{\rho}+\frac{m^2}{k}\frac{J_m(kr)}{r}\sin(\phi)\hat{\phi}+0\hat{z}[/tex]

where m is an integer, and k could satisfy to:

[tex]J_m(ka)=0[/tex] or [tex]J_m'(ka)=0[/tex] with a real.

(the apex is used for the derivative respect to r)

In this case I need to express the divergence of the field and the following integral:

[tex]\int_0^a\int_0^{2\pi}(|A_r|^2+|A_\phi|^2)r\,dr\,d\phi[/tex]

Is it possible to found simpler analytical formulas for general m for the results?

Where can I found useful relationships for the bessel integrals involved? thank you.

[tex]\vec{A}=-J'_m(kr)\cos(\phi)\hat{\rho}+\frac{m^2}{k}\frac{J_m(kr)}{r}\sin(\phi)\hat{\phi}+0\hat{z}[/tex]

where m is an integer, and k could satisfy to:

[tex]J_m(ka)=0[/tex] or [tex]J_m'(ka)=0[/tex] with a real.

(the apex is used for the derivative respect to r)

In this case I need to express the divergence of the field and the following integral:

[tex]\int_0^a\int_0^{2\pi}(|A_r|^2+|A_\phi|^2)r\,dr\,d\phi[/tex]

Is it possible to found simpler analytical formulas for general m for the results?

Where can I found useful relationships for the bessel integrals involved? thank you.

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