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

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?

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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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