1. A metal cylinder of radius a and length L has both ends held at a zero potential, and the sides are at constant potential Vo (a) Find the potential (p.6, 2) everywhere in the interior of the cylinder. Assume the cylinder is aligned with the axis and that and that the ends are located at := 0 and := L. I suggest choosing a functional form that vanishes explicitly for z= L and 2 = L.
1. A metal cylinder of radius a and length L has both ends held at a zero potential, and the sides are at constant potential Vo (a) Find the potential (p.6, 2) everywhere in the interior of the cylinder. Assume the cylinder is aligned with the axis and that and that the ends are located at := 0 and := L. I suggest choosing a functional form that vanishes explicitly for z= L and 2 = L.
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Please at least try to attempt a. Be very detailed.
Transcribed Image Text:1. A metal cylinder of radius a and length L has both ends held at a zero potential,
and the sides are at constant potential Vo
(a) Find the potential (p, 0, 2) everywhere in the interior of the cylinder.
Assume the cylinder is aligned with the z axis and that and that the ends
are located at z = 0 and z= L. I suggest choosing a functional form that
vanishes explicitly for z = L and 2 = L.
(b) Now consider the same question, but with some shifts applied:
(p. 0,2)=(p.o.z+ L/2) - Vo.
i.e., such that the center of the cylinder is now at the origin, the potential
vanishes on the sides of the cylinder, and the potential is equal to -Vo on
the ends. Find using functions that vanish explicitly on the sides of
the cylinder.
(c) Which solution of the problem is "better"? Why?
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