Insights A Physics Misconception with Gauss’ Law

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Gauss' Law is often misunderstood, particularly when transitioning from lower to upper-level electromagnetism courses. A common misconception arises when students incorrectly apply Gauss' Law to systems lacking spherical symmetry, leading to erroneous conclusions about electric fields. The discussion highlights the importance of recognizing the limitations of Gauss' Law and emphasizes the need for a solid understanding of vector calculus to properly grasp electromagnetic concepts. Many students struggle with these complexities due to oversimplified teaching methods that can hinder their learning. Addressing these misconceptions can significantly aid students in mastering electromagnetism.
Orodruin
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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.
 
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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.
 
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Orodruin said:
This is the hope. I have seen this kind of error ”more than once” here at PF.

So I’m not alone!
 
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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".
 
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Excellent thread.

Thanks
Bill
 
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Please can anyone either:- (1) point me to a derivation of the perpendicular force (Fy) between two very long parallel wires carrying steady currents utilising the formula of Gauss for the force F along the line r between 2 charges? Or alternatively (2) point out where I have gone wrong in my method? I am having problems with calculating the direction and magnitude of the force as expected from modern (Biot-Savart-Maxwell-Lorentz) formula. Here is my method and results so far:- This...

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