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

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Discussion Overview

The discussion revolves around the derivation of the electric field equation E=(2kλ)/r for an infinite line of charge, specifically how Gauss's Law applies in this context. Participants explore the relationship between different unit systems, particularly Gaussian units and their implications in electromagnetism.

Discussion Character

  • Exploratory
  • Technical explanation
  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • One participant seeks clarification on the equivalence of the expression ∫E⋅dA=4πq to Gauss's Law in the context of an infinite line of charge.
  • Another participant notes that the expression is a form of Maxwell's equations in Gaussian units, suggesting a connection to different unit systems.
  • There is a discussion about the commonality of CGS units in electricity and magnetism, with references to graduate-level texts.
  • One participant expresses a preference for Gaussian units over SI units, arguing that the former provides more elegance and intuition in theoretical electromagnetism.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the use of unit systems, with differing opinions on the merits of Gaussian versus SI units. The discussion remains unresolved regarding the implications of these units on the understanding of electromagnetism.

Contextual Notes

There are references to specific textbooks and unit systems that may not be universally familiar, indicating a potential limitation in shared knowledge among participants.

stephen8686
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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?
 
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stephen8686 said:
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.
 
Wow, I didn't even know that was a thing! Thanks. Are CGS units commonly used in Electricity and magnetism?
 
stephen8686 said:
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.
 
Well thanks a lot for the help!
 
ZapperZ said:
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 :-).
 

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