# 2.17 A long charged cylinder of linear charged density $\lambda$ is surrounded by a hollow co-axial conducting cylinder. What is the electric field in the space between the two cylinders?

The charge density of the cylinder with length l and radius r = $\lambda$

The radius of another hollow cylinder with same length = R

Now, let our gaussian surface be a cylinder with the same length and different radius r

the electric flux through Gaussian surface

$\oint E.ds=\frac{q}{\epsilon _0}$

$E.2\pi rl=\frac{\lambda l}{\epsilon _0}$

$E.=\frac{\lambda }{2\pi \epsilon _0r}$

Hence electric field ar a distance r from the axis of the cylinder is

$E=\frac{\lambda }{2\pi \epsilon _0r}$

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