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

Explanation

Let there be a long charged cylinder A of linear charge density , length l and radius a. Now, one more hollow co-axial cylinder B of same length l and radius b surrounds the cylinder A(b `gt` a)
The charge on cylinder `A,q=lamda l`
Total charge = Linear charge density × Length
This charge spreads uniformly on A and a charge -q is induced on B. Let E be the electric field produced in the space between the two cylinders. Consider a Gaussian cylindrical surface of radius r between the two given cylinders.
Electric flux linked with the Gaussian surface `int_E=int E. ds =int E.ds cos 0^@=E int ds=E times 2`
[As angle between the direction of electric field and area vector is zero]
According to Gauss’s theorem `phi=E times 2pi rl=q/e_0, E times 2pi rl=(lamda l)/e_0, E=lamda/(2pi e_0r)`