91Ó°ÊÓ

It is given that an infinitely long straight wire carries a uniform volume charge density${}^{\mathrm{λ}}$.The electric field at a distance s around the infinitely long wire has to be evaluated.

If there is a surface area enclosing a volume, possessing a charge${}^q$inside the volume then the electric field due to the surface or volume charge is given as

Here${}^q$is the elemental surface area,${}^{{\mathrm{Î\mu }}_0}$is the permittivity of free surface.

Consider a Gaussian cylinder of finite length / located at a distance symmetrically around the infinitely long wire, as shown below:

It is known that the infinitely long wire consist the linear charge of density$\mathrm{λ}$For a Gaussian cylinder of length${}^{/}$the total charge inside the Gaussian cylinder is${}^{\mathrm{λ}/}$

Apply Gauss law, on the Gaussian surface, as,

Thus the electric field at a distance s from infinitely long wire is