How does Gauss's Law relate to E=(2kλ)/r for an infinite line of charge?

[stephen8686]

I was looking for a derivation of E=(2kλ)/r for an infinite line of charge. I understood that you need to use Gauss's Law and a cylinder around the line. When looked it up, I found this: http://www.vizitsolutions.com/portfolio/gausslaw/lineCharge.html
He starts out with ∫E⋅dA=4πq. I have never seen Gauss's Law shown like this and am not sure how it is equivalent. Can someone please show me how he got 4πq from Q/ε0?

 

[ZapperZ]

I was looking for a derivation of E=(2kλ)/r for an infinite line of charge. I understood that you need to use Gauss's Law and a cylinder around the line. When looked it up, I found this: http://www.vizitsolutions.com/portfolio/gausslaw/lineCharge.html
He starts out with ∫E⋅dA=4πq. I have never seen Gauss's Law shown like this and am not sure how it is equivalent. Can someone please show me how he got 4πq from Q/ε0?

That is what is known as a form of Maxwell equation in "Gaussian units".

http://www.physicspages.com/2014/11/06/electromagnetism-in-gaussian-cgs-units/

Zz.

 

[stephen8686]

Wow, I didn't even know that was a thing! Thanks. Are CGS units commonly used in Electricity and magnetism?

 

[ZapperZ]

Wow, I didn't even know that was a thing! Thanks. Are CGS units commonly used in Electricity and magnetism?

Yes, and in fact, if you go on to take graduate level E&M and use the infamous Jackson's Classical Electromagnetism text, that was all written in cgs units.

Zz.

 

[stephen8686]

Well thanks a lot for the help!

 

[vanhees71]

Yes, and in fact, if you go on to take graduate level E&M and use the infamous Jackson's Classical Electromagnetism text, that was all written in cgs units.

Zz.

Well, and this in my opinion not infamous but rightfully famous text (in fact I think it's the best traditionally written textbook on the subject and I don't understand why anybody takes the effort to write more such traditional E&M textbooks at the graduate level when you can as well use Jackson) got worse with the 3rd edition when switching from Gaussian (the 2nd best choice of units; the best one are rationalized cgs units, aka Heaviside-Lorentz units) to SI units. Electromagnetism looses all it's elegance and physics intuition by writing it down in SI units, which are very useful for practical but very ugly for theoretical purposes :-).