A Physics Misconception with Gauss’ Law

[Orodruin]

Table of Contents
1IntroductionWhat Gauss’ law saysSpherical symmetryFailure of the argument for spherical symmetryCylinder symmetryBe careful!
Introduction
It is relatively common to see the following type of argument:
The surface area is $A$ and the enclosed charge is $Q$. The electric field strength on the...

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[PhDeezNutz]

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I kid you not. After doing very well in lower level undergrad physics I moved onto the Griffiths level class and I got a 1/30 on the first test because I applied Gauss’ Law to circular ring with linear charge density proportional to $/cos /theta$. Find the field on the axis. And since $/cos /theta$ evaluates to $0$ when integrated over $\left[ 0, 2 \pi \right]$ I thought the field was also $0$.

I really thought at the the time that Gauss’ Law was all that I needed to know. I asked my professor if the grade was a mistake and he said “no your performance was truly dismal”.

I ended up retaking the class and studied my ass off by doing damn near every problem in the first 7-8 chapters and ended up earning his respect “I saw how hard you worked and I am very pleased with your progress”.

Realizing the limitations of Gauss’ Law might be trivial for those who have had years of experience but it’s a huge stumbling block for a lot of people (not just me) making the jump from lower level E&M to upper level E&M so I’m sure some younger students will benefit greatly from this article.

 

[Orodruin]

Realizing the limitations of Gauss’ Law might be trivial for those who have had years of experience but it’s a huge stumbling block for a lot of people (not just me) making the jump from lower level E&M to upper level E&M so I’m sure some younger students will benefit greatly from this article.

This is the hope. I have seen this kind of error ”more than once” here at PF.

 

[PhDeezNutz]

This is the hope. I have seen this kind of error ”more than once” here at PF.

So I’m not alone!

 

[vanhees71]

You are not, and in my opinion it's the result of some well-meaning didadictics to "simplify" but making the subject in fact more complicated. There is some unfortunate idea in the didactics community that "math is too difficult". Of course, it's some effort to learn the math, and here it's vector calculus, which is a lot of material, but at the end it makes the physics more easy to formulate: The Maxwell equations in their "local form", i.e., as differential equations are the fundamental equations. The integral form can be easily derived from them when needed, and usually they are "more complicated" than the "local form".

 

[bhobba]

Excellent thread.

Thanks
Bill