Problem: 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).

FREE Expert Solution

Electric flux through a closed surface, from Gauss's law, is expressed as:

ϕE=E·ds=Qε0

(a)

Considering a cylinder of infinite length and imagining that a cylinder of finite length, l, is cut from this cylinder.

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Problem Details

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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