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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


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

    Laplace equation is:
    With the following boundary conditions:
    The potential is finite everywhere, especially at and as :
    And the last condition is that the potential is periodical:
    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:
    We assume a solution in the form:


    And finally:

    Solution Summary

    The expert examines infinitely long hollow conducting tube.