Question

Gauss's law help??

Figure 23-36a shows a narrow charged solid cylinder that is coaxial with a larger charged cylindrical shell. Both are nonconducting and thin and have uniform surface charge densities on their outer surfaces. Figure 23-36b gives the radial component E of the electric field versus radial distance r from the common axis. What is the linear charge density of the shell?
http://www.webassign.net/hrw/hrw7_23-36.gif
I've been working on this problem for a while but for the love of God I cannot figure it out (The answer should be in Coulombs/meter)

Answer 1

thinking out loud i would use a cylindrical Gaussian surface at r = 3.5cm. it's thin so we can do the surface at just inside the cylinder and then just outside but using r = 3.5cm for both

ok, so from Gauss' Law: \(E \times A = \dfrac{\sum Q_{enc}}{\epsilon}\)

just inside we have \(1 N/C \times 2 \pi (0.035) l = \dfrac{Q_{in}}{\epsilon}\) where "l" is just a placeholder for length of the coaxial

just oustide we have \(-2 N/C \times 2 \pi (0.035) l = \dfrac{Q_{out}}{\epsilon}\)

thus \(\Delta Q = - \pi \epsilon l \times 3 \times 0.035 \), and \(\Delta Q\) 's the charge in the outside sleeve.

i think by linear charge density they mean \(\dfrac{\Delta Q}{l}\) which is \(- \pi \epsilon \times 3 \times 0.035 \)

does that make sense/ ring bells ?