A long straight wire has fixed negative charge with a linear charge density of magnitude 4.6 nC/m. The wire is to be enclosed by a coaxial, thin-walled, nonconducting cylindrical shell of radius 2.2 cm. The shell is to have positive charge on its outside surface with a surface charge density σ that makes the net external electric field is zero. Calculate σ.

Question

Farley

Physics

8 March, 19:18

A long straight wire has fixed negative charge with a linear charge density of magnitude 4.6 nC/m. The wire is to be enclosed by a coaxial, thin-walled, nonconducting cylindrical shell of radius 2.2 cm. The shell is to have positive charge on its outside surface with a surface charge density σ that makes the net external electric field is zero. Calculate σ.

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Baldwin · Answer 1

Answer: - 33.3 * 10^9 C/m^2 (nC/m^2)

Explanation: In order to solve this problem we have to use the gaussian law, the we have:

Eoutside = 0 so teh Q inside==

the Q inside = 4.6 nC/m*L + σ * 2*π*b*L where L is the large of the Gaussian surface and b the radius of the shell.

Then we simplify and get

σ = - 4.6 / (2*π*b) = - 33.3 nC/m^2