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I've been working my way through Mathematics for Physicists by Dennery and Krzywicki and, on page 65, they assert that Gauss' law applied to a 2D cross-section along an infinite charged cylinder is:

∫E.n dl = 4πσ

where E is the electric field on the Gauss surface (a circle around the cylinder), n is the unit normal to this surface, dl is an element of length along the circumference of the Gauss surface, and σ is the charge per unit length along the cylinder.

The right side of the 2D Gauss' law should be the charge enclosed times some constant, and the charge enclosed is the circumference of the cylinder times the charge density, no? But then I get

∫E.n dl = 2πrσ (times some constant)

where r is the radius of the cylinder enclosed. Why is there no radius factor on the right hand side of the equation given in the text? Perhaps I'm misinterpreting the problem setup?