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    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.

    © BrainMass Inc. brainmass.com October 10, 2019, 12:20 am ad1c9bdddf
    https://brainmass.com/physics/system-work/infinitely-long-hollow-conducting-tube-288286

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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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