The question (in a tutorial video) was like this: find the electric field at a distance of .5m away from an infinite wire of charge density .25 micro coulumb/m. The solution used gauss law to solve this . It went "integral of vector E dot vector DA equals the charge enclosed over permittivity". Then the person said to draw a cylinder around the wire. And proceeded to calculate E field and Area of it. Now, the e field comes out perpendicularly from the surface of the cylinder. So the dot product of Vector e and vector dA (d area) should equal the magnitude of E field rimes magnitude of dA times cos theta. But theta is 90 and cos thetha is zero! How will this work?

The integral you're talking about is this:



Your question boils down to this: what is the direction of the vector ? Its direction is perpendicular to the incremental area dA. Hence and point in the same direction - they are not at right angles to each other. Hence = 1.

Oooooo! Confusion cleared. Thanks.