Q.Electric intensity outside a charged cylinder having the charge per unit length '$\lambda$' at a distance r from its axis is ____.

Gauss's law on a coaxial cylindrical Gaussian surface of radius $r$ gives $E\propto 1/r$ for a long charged cylinder/wire, with the constant fixed by the linear charge density.

For an infinitely long charged cylinder (or wire) with linear charge density $\lambda$, surrounded by a medium of dielectric constant $K$, apply Gauss's law to a coaxial cylindrical Gaussian surface of radius $r$ and length $l$ (outside the charged cylinder):

$\oint \vec E\cdot d\vec A = \frac{q_{\text{enc}}}{\epsilon_0 K}.$ …