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

$\overline{){{\mathbf{\varphi}}}_{{\mathbf{E}}}{\mathbf{=}}{\mathbf{\int}}\stackrel{\mathbf{\rightharpoonup}}{\mathbf{E}}{\mathbf{\xb7}}{\mathbf{d}}\stackrel{\mathbf{\rightharpoonup}}{\mathbf{s}}{\mathbf{=}}\frac{\mathbf{Q}}{{\mathbf{\epsilon}}_{\mathbf{0}}}}$

**(a)**

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).

Frequently Asked Questions

What scientific concept do you need to know in order to solve this problem?

Our tutors have indicated that to solve this problem you will need to apply the Electric Fields with Calculus concept. You can view video lessons to learn Electric Fields with Calculus. Or if you need more Electric Fields with Calculus practice, you can also practice Electric Fields with Calculus practice problems.