derive field due to infinitely long straight uniformly charged wire
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The resultant electric field due to these two charge elements points radially away from the charged wire and the magnitude of electric field is same at all points on the circle of radius r. From this property. We can infer that the charged wire possesses a cylindrical symmetry. Qencl=λL.
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We wish to find its electric field at a distance of r from it. Let a cylinder of radius r and height l be the Gaussian surface. Now at the top and bottom phases of cylinder i.e. its base and top E and dS are perpendicular to each other hence it does not contributes to electric flux. E = lambda / 2π(epsilon not)r.
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