(a) Derive an integral expression for the charge density (, z) induced on the outer surface of...

(a) Derive an integral expression for the charge density σ(φ, z) induced on the outer surface of a conducting tube of radius R when a point charge q is placed at a perpendicular distance s > R from the symmetry axis of the tube.

(b) Confirm that the point charge induces a total charge −q on the tube surface.

(c) Show that the angle-averaged linear charge density falls off extremely slowly with distance along the length of the tube. Specifically, show that, as z→∞,

Transcribed Image Text:

2π R 1.Th S λ(z) = R dφ σ(φ,z) ~ q ln(s/R) z ln²(z/R)