# Infinitely long hollow conducting tube

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Consider n infinitely long hollow conducting tube tht is split in half with each half held at the indicated potential.

calculate B_o, B_n, A_n

what equation would plot V(rho, pi/2).

do not need mathcad work.

attatched copy of diagram.

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Note that I used r and theta instead of rho and phi (old habits die hard)

Laplace equation is:

(1.1)

With the following boundary conditions:

(1.2)

The potential is finite everywhere, especially at and as :

(1.3)

(1.4)

And the last condition is that the potential is periodical:

(1.5)

Since the system is completely symmetric with respect to the xy plane the potential has no dependence on the z-coordinate and equation (1.1) becomes a two dimensional problem in polar coordinates:

(1.6)

We assume a solution in the form:

(1.7)

Then:

And finally:

...

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