Why does Coulomb's Law include a pi in the denominator?

[Old Guy]

Homework Statement

I'm sure I'm missing something simple here, but to the point:

I calculate the electric field a distance r from a uniform straight infinite line charge using Gauss' Law and get an answer; I do the same calculation using Coulomb's law and get the same answer but a pi remains in the denominator (that was not there in the Gauss' Law solution). I don't know how to enter the equation here, but in both answers the numerator is the linear charge density. The Gauss' Law denonminator is 2r times epsilon; Coulomb's law denominator is 2(pi)r times epsilon. Help!

Homework Equations

See above

The Attempt at a Solution

See above

 

[foxjwill]

Can you write out each of your steps? Maybe then one of us'll be able to spot the error.

 

[Old Guy]

Well, thanks for the fast response. In writing out the steps as you requested I caught a (dumb) integration error - I'm straight now. Thanks.

 

[foxjwill]

Well, thanks for the fast response. In writing out the steps as you requested I caught a (dumb) integration error - I'm straight now. Thanks.

You can't imagine how many times I've been stumped on a problem only to realize my error while explaining what I did to someone. :)