In summary, this article discusses the limitations of Gauss' Law and how it is often misunderstood and misapplied by students. The conversation in the article highlights a common error in applying Gauss' Law to problems involving spherical symmetry and emphasizes the importance of understanding the fundamental equations of electromagnetism. The hope is that by clarifying these misconceptions, students will have a better grasp of the subject and be able to apply it more effectively.
Orodruin
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topsquark, bhobba, vanhees71 and 3 others
Orodruin said:
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.

Chikitai, bhobba, Delta2 and 4 others
PhDeezNutz said:
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.

bhobba, vanhees71 and PhDeezNutz
Orodruin said:
This is the hope. I have seen this kind of error ”more than once” here at PF.

So I’m not alone!

bhobba and 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, BvU, PhDeezNutz and 2 others

Thanks
Bill

PhDeezNutz

## 1. What is Gauss' Law and how is it used in physics?

Gauss' Law is a fundamental law in physics that relates the electric flux through a closed surface to the charge enclosed within that surface. It is used to calculate the electric field at a point due to a distribution of charges, and is an important tool in understanding the behavior of electric fields.

## 2. What is the common misconception about Gauss' Law?

The most common misconception about Gauss' Law is that it only applies to symmetrical charge distributions. In reality, Gauss' Law can be used for any charge distribution, as long as the electric field can be calculated at every point on the surface of the closed surface.

## 3. How does Gauss' Law relate to Coulomb's Law?

Gauss' Law is a generalization of Coulomb's Law, which only applies to point charges. Gauss' Law allows us to calculate the electric field due to any charge distribution, not just point charges.

## 4. Can Gauss' Law be used to calculate the electric field inside a conductor?

Yes, Gauss' Law can be used to calculate the electric field inside a conductor. However, the electric field inside a conductor is always zero, so Gauss' Law is not very useful in this case.

## 5. How is Gauss' Law derived?

Gauss' Law is derived from the fundamental principles of electrostatics, including the inverse square law of electric force and the superposition principle. It can also be derived from Maxwell's equations, which describe the behavior of electric and magnetic fields.

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