Electric flux through a closed surface, from Gauss's law, is expressed as:
Considering a cylinder of infinite length and imagining that a cylinder of finite length, l, is cut from this cylinder.
An infinitely long cylindrical conductor has radius R and uniform surface charge density σ.
(a) In terms of σ and , what is the charge per unit length λ for the cylinder?
(b) In terms of s, what is the magnitude of the electric field produced by the charged cylinder at a distance r > R from its axis?
(c) Express the result of part (b) in terms of λ and show that the electric field outside the cylinder is the same as if all the charge were on the axis. Compare your result to the result for a line of charge in Example 22.6 (Section 22.4).
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