Avery long (nearly infinite) wire is made of an insulating material. the wire carries a charge, q, which is distributed evenly along the entire length of the wire, giving it a uniform linear charge density, lambda. what is the magnitude of the electric field produced by the charged wire at a radial distance s from the wire?

E= λ/ 2πε0 with radial direction

Explanation: Using the Gaussian law, we can obtain the Electric at distance r from the line of charge very large.

In this sense

The electric flux by a closed surface is: ∫E.dS= Total charge/ε0

so

at distance r the electric field is constant and surface integral is equal to the curved surface of the cilindrical Gaussian surface  around the line of charge. It was used to conduct the Gaussian Law.

this means

A= 2πr L where L is lengt of line of charge

Finally E*2 πr L = λL/ε0

Fron this  expression the electric is: E= λ/ 2πε0