Confusion created by notation in E&M

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    Confusion E&m Notation
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SUMMARY

The discussion centers on the confusion caused by the notation used in Electromagnetism (E&M) classes, particularly the multiple representations of the variable "r." Participants highlight various forms such as capital R, lowercase r, r prime, and others, which complicate understanding. The issue stems from the reliance on the Latin alphabet, leading to a lack of clarity when multiple variables are present in equations. A suggested solution is to relabel variables to more intuitive names, aiding comprehension and reducing confusion.

PREREQUISITES
  • Understanding of basic Electromagnetism concepts.
  • Familiarity with vector notation and spherical coordinates.
  • Knowledge of mathematical notation in physics, including primes and hats.
  • Experience with variable manipulation in equations.
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  • Research the use of variable notation in advanced physics, focusing on Electromagnetism.
  • Learn about the implications of using different alphabets (Greek, Cyrillic) in scientific notation.
  • Explore strategies for simplifying complex equations in physics.
  • Study the historical context of notation in physics to understand its evolution.
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Students in Electromagnetism courses, physics educators, and anyone struggling with complex notation in scientific equations.

leroyjenkens
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I just started an E&M class and right from the beginning the notation seems so confusing it has to have been done as a joke.
Trying to do a problem I run into about 10 different r's I have to keep track of.
Capital R
Lower case r
Lower case r prime
The r in spherical coordinates
The "squiggle" r (As this professor calls it. Never heard that before this class, but he talked about it like everyone knows. It's just a cursive r from what I can tell.)
"Squiggle" r hat
Normal r hat prime
"Squiggle" r with an arrow over it.
The normal r with an arrow over it
Normal r with an arrow over it prime

So when I see an equation with 3 or 4 different r's in it, my head just explodes. Why is it like this? And am I the only one who thinks this makes it confusing?
 
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This is what happens when you restrict yourself to the latin Alphabet. Try using Greek and Cyrillic letters if you run out.
 
There is a weird fascination with symmetry and making letters look the same. Euler angles were introduced to me with \xi, \zeta, \eta as indices. Integration by parts uses u and v, there is p and q for Lagrange mechanics. i and j for electrodynamics. {j,k,l} and {x,y,z} might not be so bad, but j and l are close in some handwriting as well as x and y. These things will never be reformed because we are still citing papers from 1910. The worst we had was in the discussion of collisions where I think r-prime-prime-tilda-hat was the vector of the second particle after the collision in center of mass coordinates.
 
I find it works extremely well when dealing with an unfamiliar notion to relabel each variable to something that makes sense to you, like m_{electron} instead of Z_0 for example. Then rewrite all of the equations and work with them until you feel comfortable and translate back as required.
 

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